勷勤数学•专家报告

题      目：Hydrodynamic limit for compressible Navier-Stokes-Vlasov equations

报  告  人：姚磊 教授  (邀请人：李进开)

                                             西北工业大学

时      间： 12月28日  10：00-11:00

地     点：数科院西楼114

报告人简介:

           姚磊，西北工业大学教授， 博士生导师，2010年在华中师范大学获理学博士学位。主要从事流体力学中的偏微分方程数学理论的研究，论文发表在 Math. Ann.、JMPA、Ann. I. H. Poincaré -AN、SIAM JMA、 Indiana Univ. Math. J.、M3AS等国际期刊上。

摘      要：

        We study the hydrodynamic limit of weak solutions to compressible Navier-Stokes-Vlasov equations without diffusive term in one dimension bounded domain. This work extends in some sense the previous work, [Mellet and Vasseur, Comm. Math. Phys., 281(2008)], which provided the hydrodynamic limit of weak solutions to the compressible Navier-Stokes-Vlasov-Fokker-Planck systems in three dimensions. We improve the results by taking advantage of compactness result  in one space dimension to obtain the convergence of macroscopic density of the particles  in . The proof relies on relative entropy method to obtain the corresponding strong convergence of fluid density . At last, we give a recent result about hydrodynamic limit for multidimensional compressible Navier-Stokes-Vlasov-Poisson equations with local alignment force.

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