Supercritical Degenerate Parabolic-Parabolic Keller-Segel System

Abstract:

This article presents a relationship between the sharp constant of the Sobolev inequality and the initial criterion to the global existence of degenerate parabolic-parabolic Keller-Segel system with the diffusion exponent $\frac{2n}{2+n}<m<2-\frac{2}{n}$. The global weak solution obtained in this article does not need any smallness assumption on the initial data. Furthermore, a uniform in time $L^{\infty}$ estimate of the weak solutions is obtained via the Moser iteration, where the constant in $L^p$ estimate for the gradient of the chemical concentration has been exactly formulated in order to complete the iteration process.

Biography:

Wang jinhuan, professor in School of Mathematics of Liaoning University. The doctoral degree was obtained in Dalian University of  Technology in 2009. She was a postdoctoral in Tsinghua University from 2010 to 2012. The major is the nonlinear partial differential equations. Her research interests are the Keller-Segel system in biology，the thin film equation in physics, the reaction-diffusion parabolic system, and the relationship between these models and functional inequalities etc. She has had many significant research results obtained in these fields, and many articles published in important international journals.

Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai