Lecture|June 11, 2017 (Wednesday) /11:00 am|Room 330 of Nanhai Building in College of Information Science and Technology/College of Cyber Security of Jinan University

Speaker: Professor Zhu Changjiang, South China University of Technology

ABOUT ZHU CHANG-JIANG

Zhu Changjiang, the laureate of The National Science Fund for Distinguished Young Scholars, the candidate of Program for New Century Excellent Talents in University from Ministry of Education and dean, professor and doctoral tutor of South China University of Science and Technology. Professor Zhu dedicates himself to nonlinear hyperbolic partial differential equations and related research and has published about 70 SCI papers in the international famous partial differential equation important academic journals like SIAM Journal on Mathematical Analysis, Journal de Mathématiques Pures et Appliquées, Journal of Differential Equations, Nonlinearity. He also takes charge of the well-known journals such as Kinetic and Related Models, ISRN (International Scholarly Research Network) Mathematical Analysis, Acta Mathematica Scientia, Acta Mathematica Scientia.
Contents introduction.

In this paper, we consider the large time behavior of the weak solution to the free boundary problem for one-dimensional isentropic compressible Navier-Stokes equations with degenerate viscosity and vacuum. Under appropriate smallness conditions on the initial data (initial energy), we give the optimal decay rate of the density function along with the behavior of it near the interfaces is studied. In the meanwhile, we obtain also sharper decay rates for the norms in terms of the velocity function. The proof is based on the standard line method. The key is to establish some new global-in-time weighted estimates (both in time and space) uniformly up to the vacuum boundary, which ensures the uniform convergence of the approximate solutions.This is a joint work with Guangyi Hong.

Fellow teachers and students are warmly welcomed!