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

内容簡介：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.

報告人：華南理工大學  朱長江  教授

報告人簡介：國家傑出青年基金獲得者、教育部新世紀優秀人才計劃入選者、華南理工大學理學院院長、教授，博士生導師。主要從事非線性雙曲型偏微分方程及其相關領域的研究，在國際上著名偏微分方程重要學術刊物《SIAM Journal on Mathematical Analysis》，《Journal de Mathématiques Pures et Appliquées》,《 Journal of Differential Equations》，《Nonlinearity》發表SCI論文近70篇。目前擔任《Kinetic and Related Models》、《ISRN（International Scholarly Research Network） Mathematical Analysis》、《Acta Mathematica Scientia》、《數學物理學報》期刊編委。

時  間：2017年6月7日（周三）上午11：00始

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