Infinite time aggregation for the critical Patlak‐Keller‐Segel model in ℝ2

By Adrien Blanchet, José Antonio Carrillo, Nader Masmoudi. 2007

151 citations recorded by the source corpus.

Subfields: Finance, Modeling and Simulation, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/62c48618698cd9c7b226b83d99e07923d0ae612e

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Citations in the corpus

A coupled Keller–Segel–Stokes model: global existence for small initial data and blow-up delay (2012, unknown): “For more references on the general Keller–Segel system, the interested reader can refer to recent work [4,5,10].”
Functional inequalities, thick tails and asymptotics for the critical mass Patlak–Keller–Segel model (2010, methodology): “Moreover, [6] proves that every such solution blows up at infinite time.”
Global Solutions to the Coupled Chemotaxis-Fluid Equations (2010, background): “The further literature on the Keller-Segel model is indeed huge and thus out of the scope of this paper; see recent work [1, 2, 5] and references therein.”
Blow-up, Concentration Phenomenon and Global Existence for the Keller–Segel Model in High Dimension (2010, methodology): “1 from the previous a-priori estimates, we follow a quite standard procedure, used in the context of Keller-Segel system for example in [12, 16, 21, 22].”
Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations (2011, methodology): “In fact, the classical Patlak-Keller-Segel [38, 26] system, see [12, 10, 11], corresponds to the choice of the Newtonian potential in R2 as interaction, W = 1 2π log |x|, with linear diffusion.”
Local and global well-posedness for aggregation equations and Patlak–Keller–Segel models with degenerate diffusion (2010, methodology): “See [27, 10, 14] for the corresponding result for classical 2D PKS.”
Global existence for the Cauchy problem of the parabolic–parabolic Keller–Segel system on the plane (2012, unknown): “If m(u0; R2) = 8π , then the solution of (2) exists globally in time [4,5].”
Refined asymptotics for the subcritical Keller-Segel system and related functional inequalities (2010, background): “Solutions having finite initial second moment concentrate in infinite time towards the Dirac mass δ0 [10, 5, 22].”
The parabolic-parabolic Keller-Segel model in R2 (2008, background): “when the initial mass M equals the threshold value ([5, 3]).”
A coupled chemotaxis-fluid model: Global existence (2011, unknown): “For more references on the general Keller–Segel system, the interested reader can refer to recent work [1,2,5].”
Chemotaxis-fluid coupled model for swimming bacteria with nonlinear diffusion: Global existence and asymptotic behavior (2010, methodology): “For more references on the general Keller-Segel system, the interested reader can refer to recent work [2, 3, 8].”