H\"older regularity and Uniqueness theorem on weak solutions to the degenerate Keller-Segel system
Analysis of PDEs
2015-03-26 v1
Abstract
In this paper, we present local H\"older estimates for the degenerate Keller-Segel system \eqref{eq-cases-aligned-main-problem-of-Keller-Segel-System} below in the range of and before a blow-up of solutions. To deal with difficulties caused by the degeneracy of the operator, we find uniform estimates depending sup-norm of the density function and modified the energy estimates and intrinsic scales considered in Porous Medium Equation. As its application, the uniqueness of weak solution to \eqref{eq-cases-aligned-main-problem-of-Keller-Segel-System} is also showed in the class of H\"older continuous functions by proving -contraction in this class.
Keywords
Cite
@article{arxiv.1503.07268,
title = {H\"older regularity and Uniqueness theorem on weak solutions to the degenerate Keller-Segel system},
author = {Sunghoon Kim and Ki-Ahm Lee},
journal= {arXiv preprint arXiv:1503.07268},
year = {2015}
}
Comments
23 pages