Refined Asymptotics for the subcritical Keller-Segel system and Related Functional Inequalities
Analysis of PDEs
2010-07-26 v1
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 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 one-dimensional equation is a contraction with respect to Fourier distance in the subcritical case.
Keywords
Cite
@article{arxiv.1007.2837,
title = {Refined Asymptotics for the subcritical Keller-Segel system and Related Functional Inequalities},
author = {Vincent Calvez and José Antonio Carrillo},
journal= {arXiv preprint arXiv:1007.2837},
year = {2010}
}