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oai:recercat.cat:2072/4527422024-06-06T09:48:09Zcom_2072_98col_2072_378195

00925njm 22002777a 4500 dc Calvez, Vincent author Carrillo de la Plata, José Antonio author Centre de Recerca Matemàtica author 2010 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. Desigualtats (Matemàtica) Equacions diferencials Refined asymptotics for the subcritical Keller-Segel system and related functional inequalities