题  目：Optimal decay rates on compressible Navier-Stokes equations with degenerate viscosity and vacuum

内容简介：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.

报告人：华南理工大学  朱长江  教授

报告人简介：国家杰出青年基金获得者、教育部新世纪优秀人才计划入选者、华南理工大学理学院院长、教授，博士生导师。主要从事非线性双曲型偏微分方程及其相关领域的研究，在国际上著名偏微分方程重要学术刊物《SIAM Journal on Mathematical Analysis》，《Journal de Mathématiques Pures et Appliquées》,《 Journal of Differential Equations》，《Nonlinearity》发表SCI论文近70篇。目前担任《Kinetic and Related Models》、《ISRN（International Scholarly Research Network） Mathematical Analysis》、《Acta Mathematica Scientia》、《数学物理学报》期刊编委。

时  间：2017年6月7日（周三）上午11：00始

地  点：南海楼330室

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2017年6月5日