On a parabolic logarithmic Sobolev inequality
Analysis of PDEs
2009-03-10 v1
Abstract
In order to extend the blow-up criterion of solutions to the Euler equations, Kozono and Taniuchi have proved a logarithmic Sobolev inequality by means of isotropic (elliptic) norm. In this paper, we show a parabolic version of the Kozono-Taniuchi inequality by means of anisotropic (parabolic) norm. More precisely we give an upper bound for the norm of a function in terms of its parabolic norm, up to a logarithmic correction involving its norm in some Sobolev space. As an application, we also explain how to apply this inequality in order to establish a long-time existence result for a class of nonlinear parabolic problems.
Cite
@article{arxiv.0903.1436,
title = {On a parabolic logarithmic Sobolev inequality},
author = {H. Ibrahim and R. Monneau},
journal= {arXiv preprint arXiv:0903.1436},
year = {2009}
}