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Paper Citation Record · LEDGER

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions

As of 11 August 2026, this Paper Citation Record lists 51 of 51 outbound references and 4 inbound Pith citation observations for arXiv:2501.07073.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2501.07073 v2

Coverage vector

measured 51 of 51 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T20:53:14.613646Z

measured 55 of 55 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+00:00

measured 4 of 4 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T17:25:00.700966Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-05-10T09:18:32.752641Z

Reference resolution

51 of 51 outbound references displayed

  • verified exact1
  • verified fuzzy34
  • unresolved16
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 99484946-d352-4675-986e-d29968c137b5 · outbound

This paper cites Bahouri, J.-Y.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Bahouri, J.-Y

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:15.243995Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.412791Z digest=sha256:5ce1d0a30fdceec72973c19ab0cbc986323b929459dfaa4bd06bdc579fe62cca

Observation 91a7b983-6589-4b75-9435-f853f1004542 · outbound

This paper cites Biler , Singularities of solutions to chemotaxis systems , vol.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Biler , Singularities of solutions to chemotaxis systems , vol

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:15.226794Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.417406Z digest=sha256:ed0db3984629b56c02d741fe99b4e020a9046026760cb536f12fe5d3b1b6248d

Observation cee3ff9b-b5cb-4cb3-bb56-25426dbcb27a · outbound

This paper cites Biler, I.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Biler, I

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:15.212556Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.421463Z digest=sha256:216c647be40b0eb7ffdf9b56352d13ae9fce509015ee1e7599ebdf70343d1e20

Observation d7466eb7-9755-45b6-b6f4-d10f61006cf3 · outbound

This paper cites Blanchet, J.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Blanchet, J

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:15.201040Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.425557Z digest=sha256:72fc785ca171b8f1f0dc9151609c8f695cee5b6fa24eccd5b352f1ec584496ec

Observation 9029aea2-8559-4e4f-b8f0-68290b980208 · outbound

This paper cites an unresolved cited work.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Unresolved cited work

Reference 5

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:53:15.190196Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.429636Z digest=sha256:dd851eb43f8a19efee7d3e102f9374b847df09d8461ed24bbb30f6454bbb16ff

Observation 4f3ff6b8-8230-4420-88ad-32ff0b62551a · outbound

This paper cites Existence of finite time blow-up in Keller-Segel system.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Existence of finite time blow-up in Keller-Segel system

Reference 6

Resolution
unresolved
no resolver link, observed 2026-08-10T20:53:14.434780Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-10T20:53:14.434780Z digest=sha256:69502e58e3a8cabb72981dd2b077e25dae8449abbeb3544f585313f57ad1de3c

Observation c609a4b3-9dbb-4a24-ad72-8b3ace43ba1a · outbound

This paper cites an unresolved cited work.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:53:15.178832Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.439683Z digest=sha256:54a50304ee93f4c7aa58521c2b4fdccc098fe866060a29038dad44f57d5d2a24

Observation f49d4bcb-a9c6-4d7f-9d64-614ca44f46fb · outbound

This paper cites Collot, T.-E.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Collot, T.-E

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:15.168023Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.443522Z digest=sha256:7f7cfe3f32dfab3a552b2215d846bdb4ec88f668dbcaa18103576987f79ab77f

Observation ffab3965-5d0f-4221-a066-4cf9ffd44d9b · outbound

This paper cites PDE, 8 (2022), pp.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions PDE, 8 (2022), pp

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:15.156552Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.447287Z digest=sha256:7cd392ec368de60d3cf4fe8d7d2e885a7ada5677eb4f22cc1d056861cdf8b718

Observation 9442e68a-4721-4f62-b3d1-ccba69871c9c · outbound

This paper cites an unresolved cited work.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Unresolved cited work

Reference 10

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:53:15.145374Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.451016Z digest=sha256:c17d083caef501b2db1a93245b0c1856b88ec9bac4eb78979157d687613125a8

Observation 12f8badb-1283-4fe2-b4cd-fa5921e0c879 · outbound

This paper cites Singularity formed by the collision of two collapsing solitons in interaction for the 2D Keller-Segel system.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Singularity formed by the collision of two collapsing solitons in interaction for the 2D Keller-Segel system

Reference 11

Resolution
unresolved
no resolver link, observed 2026-08-10T20:53:14.454871Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-10T20:53:14.454871Z digest=sha256:a905c91faad32a53c9bce5e5e86d464a3c9a966a1f960a8244b245661c2c2397

Observation 2eeafda7-8221-420f-a2a7-bae64c3277d4 · outbound

This paper cites Collot, F.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Collot, F

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:15.134116Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.459620Z digest=sha256:292f3e3aeb6f84671b82ca07dee5980cdd6d221f8e02de31fc4e526dd09e7efb

Observation 9a3231ca-745a-478d-ad1b-9b61d34a4b01 · outbound

This paper cites Collot, P.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Collot, P

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:15.121284Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.463402Z digest=sha256:0fd3c9d9899133bfb63a75f9d19adf1e1b64ead356bc7c241d31f74215c059bc

Observation 2278297d-fc93-46d6-b36c-838e6566f179 · outbound

This paper cites On the stability of Type I self-similar blowups for the Keller-Segel system in three dimensions and higher.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions On the stability of Type I self-similar blowups for the Keller-Segel system in three dimensions and higher

Reference 14

Resolution
unresolved
no resolver link, observed 2026-08-10T20:53:14.467359Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-10T20:53:14.467359Z digest=sha256:13ba540ae536c1ca4835b04ccc905b0c68f5dbea7254278d8859e8a510623a93

Observation f13574c2-21a1-4b37-af18-5a603808c1a3 · outbound

This paper cites Corrias, B.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Corrias, B

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:15.110113Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.471801Z digest=sha256:1c788701d75a9db1e71d27f28f0598b1f20412315d0d7c50252f9d25e1dc83be

Observation c5699e6e-0add-4fcf-ac23-cfc7fc4be291 · outbound

This paper cites Costin, R.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Costin, R

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:15.098567Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.475693Z digest=sha256:7242d9af6667ae4dc478f1e60aaf69af966ac0c33c617a4b82aca8daaa4451ef

Observation 9f03f095-5999-43bf-94f5-2bc4d53c2047 · outbound

This paper cites Costin, R.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Costin, R

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:15.087627Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.479340Z digest=sha256:51c8fa263a523c355eeaa134fe9db59d75ce18f85e2e5b09f41f89c8d362cc2a

Observation 92042c63-0f70-403d-8109-251418a5ec4c · outbound

This paper cites Demanet and W.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Demanet and W

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:15.076590Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.482816Z digest=sha256:8a56feb21a914b6f665d65d8da8e4e973ca3e10725a8d5f11dcb0be8adcf0870

Observation 1c86bff0-1fd5-47dd-81b0-f3913cd9f11a · outbound

This paper cites Dolbeault and B.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Dolbeault and B

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:15.065838Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.485929Z digest=sha256:7f8cda5751ed532445246c0cf828facdd3996eacfceacd3bc9d20ab211176c52

Observation 966aaf0f-8473-4f6e-900f-53282fcd838e · outbound

This paper cites Donninger , Spectral theory and self-similar blowup in wave equations , Bull.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Donninger , Spectral theory and self-similar blowup in wave equations , Bull

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:15.054459Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.489345Z digest=sha256:7ea0c069f32ec40af1431356ca1d17ba9012bf8be20ad71d670d1e742f88e6e4

Observation 49e87169-e856-4c8a-9fd9-0f3ef6a1b9db · outbound

This paper cites Donninger and B.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Donninger and B

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:15.041414Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.492549Z digest=sha256:b8256510b8ef3a6f0eecb7e57f6914f5d7b5d79c658689253467fd87bdd7b426

Observation 7681552c-3bc2-4b74-94be-43379e76dc92 · outbound

This paper cites Engel and R.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Engel and R

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:15.028767Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.495611Z digest=sha256:f4e8f41ca96fe096a636a4c35a276d33b87415f80514aa7b7d7ddb4b589cad94

Observation 84bd738f-36b5-48e0-befc-3df6dee85e23 · outbound

This paper cites Giga and R.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Giga and R

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:15.015242Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.498831Z digest=sha256:0feca5b7bd9f5f8ea2d3a52f93c7954725a37856e15880ed0df0735370103691

Observation 72de44a6-17f5-4eff-b582-b2222d369dcc · outbound

This paper cites an unresolved cited work.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Unresolved cited work

Reference 25

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:53:15.003347Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.502147Z digest=sha256:3446cbbd6602af64f381df2d8e066b726f5c6e16071909b6a18d2af55eb2dc61

Observation c09a44b9-b454-4937-a6c4-01ed20ef1b2c · outbound

This paper cites Glogić and B.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Glogić and B

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:14.990290Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.505508Z digest=sha256:f520a30736d4f42296ca8248fd4cb21b21ff322a3564edea26174a9998f32997

Observation f49ff781-f640-4d26-9fec-86e24ff5d807 · outbound

This paper cites an unresolved cited work.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Unresolved cited work

Reference 27

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:53:14.978553Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.509005Z digest=sha256:8726dd243577f8138e1ada4dd86595721eebe74b0b78b959eec47a56ccb5b2b2

Observation da79da24-e577-4058-b948-5c1377f188cc · outbound

This paper cites an unresolved cited work.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Unresolved cited work

Reference 28

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:53:14.966784Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.512317Z digest=sha256:cfd6d588fd1e82e0dffaefa6bcacf342d045e61502a1b396c6c5542851087c7d

Observation 841eb1d6-9024-4d7e-9e1c-bb04e0946f2f · outbound

This paper cites Horstmann , From 1970 until present: the Keller-Segel model in chemotax is and its con- sequences.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Horstmann , From 1970 until present: the Keller-Segel model in chemotax is and its con- sequences

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:14.954566Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.516201Z digest=sha256:da38cfe407af28b5a2a77431890cb001c163d327f12081c78aed0010a44f085d

Observation 51463589-ae76-4b69-b638-86786104fc75 · outbound

This paper cites II, Jahresber.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions II, Jahresber

Reference 30

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:14.943574Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.520045Z digest=sha256:ce6defe102484b8ef2c1c3ccf4789d287f346081ab860dd59c405e2857fd8447

Observation 007fc052-5534-442a-b3c5-09f33eb40a82 · outbound

This paper cites an unresolved cited work.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Unresolved cited work

Reference 31

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:53:14.932997Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.524243Z digest=sha256:310e9866a3abc7961bd70b37d8df8c120adf89ee749f8986faefc45610cc9433

Observation 9e5d4d13-5a6a-478c-a01f-2cee7474b898 · outbound

This paper cites Lenzmann , Uniqueness of ground states for pseudorelativistic Hartre e equations , Anal.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Lenzmann , Uniqueness of ground states for pseudorelativistic Hartre e equations , Anal

Reference 32

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:14.922192Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.528060Z digest=sha256:6208e233fb574d51129c0d42b9a3fe26f7605c291c322fcc5d74105182babdb5

Observation acdd27d9-29e1-4253-8e01-d8ec4405b358 · outbound

This paper cites an unresolved cited work.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Unresolved cited work

Reference 33

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:53:14.910455Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.532038Z digest=sha256:03a453607a003ced83517a4f1e0465bbc090161b3e5d724b27226d2b06b7a1f2

Observation 2cc1d38d-5e63-4a10-ac6a-d59e266a6a4b · outbound

This paper cites Pure Appl.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Pure Appl

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:14.898169Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.535904Z digest=sha256:c4980aefac54f180153e1e3e02218d33d6d34de507b03c3e62db35b97348148e

Observation 1160a233-c180-4eed-b393-3ce047d9f8de · outbound

This paper cites Li , Mode stability for self-similar blowup of L2 slightly supercritical NLS , in preparation.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Li , Mode stability for self-similar blowup of L2 slightly supercritical NLS , in preparation

Reference 35

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:14.887369Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.540173Z digest=sha256:ad7cedb48db43df537a72df76d32e9464c0fa047bae470d6be6cfe6e90e90a19

Observation 11d09e64-c0f8-4d7e-9dc0-d65faed9071c · outbound

This paper cites On stability of self-similar blowup for mass supercritical NLS.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions On stability of self-similar blowup for mass supercritical NLS

Reference 36

Resolution
unresolved
no resolver link, observed 2026-08-10T20:53:14.544074Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-10T20:53:14.544074Z digest=sha256:755586e3f470ccc7d8717c4d81da90b7cd373e28977e4a3a58503c60aeec4050

Observation c2caca7d-61ec-4d4a-b347-f0153c935990 · outbound

This paper cites Finite-time blowup for Keller-Segel-Navier-Stokes system in three dimensions.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Finite-time blowup for Keller-Segel-Navier-Stokes system in three dimensions

Reference 37

Resolution
verified exact
local_arxiv, observed 2026-08-10T20:53:14.669019Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.548549Z digest=sha256:8c0a740ec9f7165d3c8b0898a9264a0452d149a82a4985347907530c87039a7f

Observation d0948709-f8d7-4131-bc74-0b9714ff851e · outbound

This paper cites Merle, P.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Merle, P

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:14.876320Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.553072Z digest=sha256:554a483a9ffad5aac55587bc3100f2e0f16a86e3b520eb333e7bab02e3d631d4

Observation e7b91d63-4e6e-4790-8b8c-30941eb3a4df · outbound

This paper cites Nagai , Blow-up of radially symmetric solutions to a chemotaxis sys tem, Adv.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Nagai , Blow-up of radially symmetric solutions to a chemotaxis sys tem, Adv

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:14.866162Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.557106Z digest=sha256:d5204d086d95fad84dc76e3d4bf7e1232565b2e400802ef5db799256e47542de

Observation 742ea09c-7547-4332-b8ca-09b17f39bd78 · outbound

This paper cites Korean Math.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Korean Math

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:14.855010Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.561186Z digest=sha256:b68626dfcaeae8bbab732e5c8a5bc222f5aa2aee30ed9ff7138f1b7aeda41a0e

Observation e535cbf9-f0c1-48cf-ac80-f03b1ec9b9d4 · outbound

This paper cites Naito and T.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Naito and T

Reference 41

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:14.844914Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.564993Z digest=sha256:22a46e33a0ded54fccb129f30b59f6199212bbd66e7414701935ef9845766dac

Observation de800116-643b-41df-b666-c81bcdba3650 · outbound

This paper cites Nakanishi and W.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Nakanishi and W

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:14.832765Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.568987Z digest=sha256:ab60917eedcfb0b89bd40dd23533021870b4d88dd157e79083a49c0d806d8150

Observation 795def4c-500c-412d-a522-01aec288e58c · outbound

This paper cites Construction of type I-Log blowup for the Keller-Segel system in dimensions $3$ and $4$.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Construction of type I-Log blowup for the Keller-Segel system in dimensions $3$ and $4$

Reference 43

Resolution
unresolved
no resolver link, observed 2026-08-10T20:53:14.574234Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-10T20:53:14.574234Z digest=sha256:07dff06e9dd2323227b6d0b126b44fa767d0f6e7f2b6f1ffa23b61f31947dcf0

Observation 0396e611-2c2f-499e-b5ed-7228315d2d8c · outbound

This paper cites Oga w a and H.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Oga w a and H

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:14.821393Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.578842Z digest=sha256:774dfde98523490fdc341c8576a46ade3a864c42b9cc6d44fd0f18964c582017

Observation 4e49233d-4737-475c-9086-63bd236ad656 · outbound

This paper cites Perelman , On the formation of singularities in solutions of the critic al nonlinear Schrödinger equation, Ann.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Perelman , On the formation of singularities in solutions of the critic al nonlinear Schrödinger equation, Ann

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:14.810148Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.583081Z digest=sha256:66181cef1d42919f34c9b79cbf605dacd9a19a26aa8fe73ce4a2ebfafd77018b

Observation 8274089a-f64f-47c3-a618-e398395b4413 · outbound

This paper cites Raphaël and R.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Raphaël and R

Reference 46

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:14.798929Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.587264Z digest=sha256:d7c1448ff8e418ef22616d705c3200fc22dd1b0afa2457db03782004fadf8c59

Observation ea517f9c-ba30-4f0b-bc3d-aaff31d7e5e0 · outbound

This paper cites Reed and B.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Reed and B

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:14.787119Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.591400Z digest=sha256:6e9c2206a600d55b86a200d0c0df0b0d4a28257961dfaa7cf31d789aebab73e0

Observation ccc1c31e-0191-43de-b7a1-83d1bbdf9cd5 · outbound

This paper cites Simon , Harmonic analysis.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Simon , Harmonic analysis

Reference 48

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:14.774751Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.595519Z digest=sha256:bc3c8e33dd575e037427eb71333397ed893f5189c1abbc4431d64c340d679d1c

Observation 542e915d-fc55-49d5-bbe7-6dcbb75d2aa9 · outbound

This paper cites Souplet and M.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Souplet and M

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:53:14.763227Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.599618Z digest=sha256:52e263e46f095706b673fe7f9d7aea60a8180500ad2a9438f82d6f1b5c74ac5a

Observation 129faebb-5f2a-4ce4-9244-f78ea3f3bd0f · outbound

This paper cites an unresolved cited work.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Unresolved cited work

Reference 50

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:53:14.751418Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.603892Z digest=sha256:13a7ab1e82dd8c476df5f8997d6277c4af312db06efd542dc94c0c8548864e11

Observation c0b93c86-1b89-4eda-a4ab-7420b63b074b · outbound

This paper cites an unresolved cited work.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Unresolved cited work

Reference 51

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:53:14.738021Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.609224Z digest=sha256:d69ab167efafd85ee82b932ffac47d5a5eb16451526ae747c1a7363ea008ea00

Observation 47d26cf9-767b-4223-87aa-fac166777d07 · outbound

This paper cites an unresolved cited work.

Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions Unresolved cited work

Reference 52

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:53:14.726177Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-10T20:53:14.613646Z digest=sha256:82184557efc860bce92833dd0cff6e629b8a579850223f3ac0b7d311a7ecc807

Pith citing papers

Observation 9afe58b9-d730-49da-95dd-5695727b4078 · inbound

Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum cites this paper.

Mode stability for self-similar blowup of slightly supercritical NLS: I. low-energy spectrum Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions

Reference 32

Resolution
unresolved
no resolver link, observed 2026-08-06T17:25:00.700966Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T17:25:00.700966Z digest=sha256:058b0d70d03cc1ea0cf316e07a90747fbe39ea1147f3818b9c1f8f17a6035c5e

Observation 18af0467-5150-460b-8426-b1ff14469bb3 · inbound

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system cites this paper.

Finite-time blow-up for the three dimensional axially symmetric Keller-Segel system Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions

Reference 62

Resolution
unresolved
no resolver link, observed 2026-08-05T21:48:41.642972Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-05T21:48:41.642972Z digest=sha256:68c31cc192f32d8c21ca1f9eedb9740dc535600438ee7249b021ad03b6de1ead

Observation 5a5d66f6-da47-40bd-8818-4b1dd595dfe0 · inbound

Singularity Formation: Synergy in Theoretical, Numerical and Machine Learning Approaches cites this paper.

Singularity Formation: Synergy in Theoretical, Numerical and Machine Learning Approaches Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions

Reference 214

Resolution
verified exact
arxiv_id, observed 2026-05-10T09:18:32.755448Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-05-10T07:13:10.140500Z digest=sha256:7905f88be6205936c075ad9ea309a45d740be63e9527314c521a6115056fbc60

Observation d42bc6b1-7fc7-4b21-ae14-ac2538833a9f · inbound

Finite time blow-up for an inhomogeneous parabolic equation cites this paper.

Finite time blow-up for an inhomogeneous parabolic equation Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions

Reference 25

Resolution
unresolved
no resolver link, observed 2026-07-14T06:33:18.586775Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-07-14T06:33:18.586775Z digest=sha256:651857eda894e88ace7968dabba408dbd4e95f1e4055997172295e376449c5c5