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Refined asymptotics for the subcritical Keller-Segel system and related functional inequalities
Calvez, Vincent; Carrillo, José A.
Centre de Recerca Matemàtica
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 onedimensional equation is a contraction with respect to Fourier distance in the subcritical case.
2010-07
517 - Anàlisi
Desigualtats (Matemàtica)
Equacions diferencials
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