In dimensions n ≥ 3, radially symmetric solutions to the parabolic-elliptic Keller-Segel system form a Dirac mass at the origin continuously via a minimal measure-valued solution, with the singular mass θ(t) increasing strictly and absorbing the entire mass asymptotically.
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Global existence of bounded solutions for generalized Hillen-Painter chemotaxis systems in R^2 is established for large Couette flow amplitude via frequency decomposition, removing prior mass thresholds.
Absence of critical mass phenomena in 1D critical quasilinear Keller-Segel systems for m ≤ -1, with all solutions globally bounded.
citing papers explorer
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Formation and Behavior of Dirac Singularities in the Parabolic-Elliptic Keller-Segel System in Dimensions $n\geq 3$
In dimensions n ≥ 3, radially symmetric solutions to the parabolic-elliptic Keller-Segel system form a Dirac mass at the origin continuously via a minimal measure-valued solution, with the singular mass θ(t) increasing strictly and absorbing the entire mass asymptotically.
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Global bounded solutions for a class of generalized Hillen-Painter models near Couette flow in $\mathbb{R}^2$
Global existence of bounded solutions for generalized Hillen-Painter chemotaxis systems in R^2 is established for large Couette flow amplitude via frequency decomposition, removing prior mass thresholds.
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Absence of critical mass phenomena in one-dimensional critical quasilinear Keller-Segel systems
Absence of critical mass phenomena in 1D critical quasilinear Keller-Segel systems for m ≤ -1, with all solutions globally bounded.