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Elsevier, Comptes Rendus Mathématique, 21-22(350), p. 949-954

DOI: 10.1016/j.crma.2012.10.023

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A functional framework for the Keller–Segel system: Logarithmic Hardy–Littlewood–Sobolev and related spectral gap inequalities

Journal article published in 2012 by Jean Dolbeault ORCID, Juan Campos Serrano, Juan Campos
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This paper is available in a repository.

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Abstract

This Note is devoted to several inequalities deduced from a special form of the logarithmic Hardy-Littlewood-Sobolev, which is well adapted to the characterization of stationary solutions of a Keller-Segel system written in self-similar variables, in case of a subcritical mass. For the corresponding evolution problem, such functional inequalities play an important role for identifying the rate of convergence of the solutions towards the stationary solution with same mass. (c) 2012 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.