Refined asymptotics for the subcritical Keller-Segel system and related functional inequalities
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- by Vincent Calvez and José Antonio Carrillo PDF
- Proc. Amer. Math. Soc. 140 (2012), 3515-3530 Request permission
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 one-dimensional equation is a contraction with respect to Fourier distance in the subcritical case.References
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Additional Information
- Vincent Calvez
- Affiliation: École Normale Supérieure de Lyon, UMR CNRS 5669 “Unité de Mathématiques Pures et Appliquées”, 46 allée d’Italie, F-69364 Lyon Cedex 07, France
- Email: vincent.calvez@ens-lyon.fr
- José Antonio Carrillo
- Affiliation: Institució Catalana de Recerca i Estudis Avançats and Departament de Matemàtiques, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Spain
- ORCID: 0000-0001-8819-4660
- Email: carrillo@mat.uab.es
- Received by editor(s): July 16, 2010
- Received by editor(s) in revised form: April 12, 2011
- Published electronically: February 23, 2012
- Communicated by: Walter Craig
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 3515-3530
- MSC (2010): Primary 35B40, 92C17
- DOI: https://doi.org/10.1090/S0002-9939-2012-11306-1
- MathSciNet review: 2929020