报告题目:  Relaxed Euler systems and convergence to compressible Navier-Stokes equations

报告人:   彭跃军 教授 （法国克莱蒙奥弗涅大学）

报告摘要：We consider the approximation of Navier-Stokes equations for a Newtonian fluid by Euler type systems with relaxation both in compressible and incompressible cases. This requires to decompose the second-order derivative terms of the velocity into first-order ones. Usual decompositions lead to approximate systems with tensor variables. We construct approximate systems with vector variables by using Hurwitz-Radon matrices, so that the systems are written in the standard form of symmetrizable hyperbolic systems. For smooth solutions, we prove the convergence of the approximate systems to the Navier-Stokes equations in uniform time intervals. Global convergence in time holds if the initial data are near constant equilibrium states of the systems. The convergence results are established not only for the approximate systems with vector variables but also for those with tensor variables.

报告人简介：彭跃军，法国克莱蒙奥佛涅大学(Université Clermont Auvergne)数学系教授。彭跃军教授于1986年在复旦大学数学系获得硕士学位，导师为李大潜院士，于1992年在法国里昂第一大学数学系，法国里昂高等师范学校数学系获得博士学位，导师为Denis SERRE教授。彭跃军教授的主要研究方向包括一维非线性守恒律方程组的熵解，高维非线性双曲型偏微分方程组的光滑解和渐近分析，等离子体和半导体模型的数学分析等；截止目前，彭跃军教授已发表专著一部，SCI数学论文90多篇，杂志包括Ann. Inst. H. Poincaré Anal. Non Linéaire, Ann. Scuola. Norm. Pisa, Communication PDE, Inverse Problems, J. Diff. Equations, J. Math. Pures Appl., SIAM J. Math. Analysis等国际高水平期刊。

报告时间: 2022.11.3(周四) 下午 3:00-5:00

报告地点: #腾讯会议：290 297 389，会议密码：1103