Refined Asymptotics for the subcritical Keller-Segel system and Related Functional Inequalities

Vincent Calvez 1, 2 José Antonio Carrillo 3
2 NUMED - Numerical Medicine
UMPA-ENSL - Unité de Mathématiques Pures et Appliquées, Inria Grenoble - Rhône-Alpes
Abstract : We analyze the rate of convergence towards self-similarity for the subcritical Keller-Segel system in the radially symmetric two-dimensional case and in the corresponding one-dimensional case for logarithmic interaction. We measure convergence in Wasserstein distance. The rate of convergence towards self-similarity does not degenerate as we approach the critical case. As a byproduct, we obtain a proof of the logarithmic Hardy-Littlewood-Sobolev inequality in the one dimensional and radially symmetric two dimensional case based on optimal transport arguments. In addition we prove that the one-dimensional equation is a contraction with respect to Fourier distance in the subcritical case.
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Submitted on : Friday, July 16, 2010 - 6:50:58 PM
Last modification on : Tuesday, November 19, 2019 - 10:29:19 AM
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  • ARXIV : 1007.2837

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Vincent Calvez, José Antonio Carrillo. Refined Asymptotics for the subcritical Keller-Segel system and Related Functional Inequalities. 2010. ⟨hal-00503203⟩

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