Global existence of strong solutions for initial mass ≤ 8π in the 2D Patlak-Keller-Segel-Navier-Stokes system, independent of velocity norm.
Stable blow-up dynamic for the parabolic-parabolic Patlak-Keller-Segel model
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abstract
We consider the parabolic-parabolic two-dimensional Patlak-Keller-Segel problem. We prove the existence of stable blow-up dynamics in finite time in the radial case. We extend in this article the result of [36] for the parabolic-elliptic case.
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math.AP 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Near any blow-up point in the planar Keller-Segel system, the localized L log L norm of u satisfies limsup (1/ln(T/(T-t))) * integral >= delta_0 > 0 as t approaches the blow-up time T.
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Critical mass threshold for the 2D Patlak-Keller-Segel-Navier-Stokes system
Global existence of strong solutions for initial mass ≤ 8π in the 2D Patlak-Keller-Segel-Navier-Stokes system, independent of velocity norm.
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Refined temporal asymptotics near blow-up points in the planar Keller-Segel system
Near any blow-up point in the planar Keller-Segel system, the localized L log L norm of u satisfies limsup (1/ln(T/(T-t))) * integral >= delta_0 > 0 as t approaches the blow-up time T.