Refined asymptotics for the subcritical Keller-Segel system and related functional inequalities

Vincent Calvez, José Antonio Carrillo

Research output: Contribution to journalArticleResearchpeer-review

23 Citations (Scopus)

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 the 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 cases based on optimal transport arguments. In addition we prove that the onedimensional equation is a contraction with respect to Fourier distance in the subcritical case. ©2012 American Mathematical Society.
Original languageEnglish
Pages (from-to)3515-3530
JournalProceedings of the American Mathematical Society
Volume140
Issue number10
DOIs
Publication statusPublished - 2 Jul 2012

Fingerprint Dive into the research topics of 'Refined asymptotics for the subcritical Keller-Segel system and related functional inequalities'. Together they form a unique fingerprint.

Cite this