主讲人简介：

彭跃军现为法国克莱蒙奥佛涅大学特级教授，复旦大学数学系学士和硕士，法国里昂第一大学博士，曾在法国奥尔良大学和波尔多第一大学担任讲师，在法国布莱兹帕斯卡大学担任教授。彭跃军教授的主要研究领域包括一维守恒律方程组的熵解，高维拟线性双曲型偏微分方程组的光滑解的适定性和渐近分析，等离子体和半导体模型的数学分析和数值模拟，到目前为止，彭跃军教授已发表专著一部，SCI数学论文90多篇。

内容摘要：

We study the approximation of Navier-Stokes equations for a Newtonian fluid by Euler type systems with relaxation. This requires to decompose the second-order derivative terms of the velocity into first-order ones. If the Maxwell laws are concerned, the decompositions lead to approximate systems with scalar, vector and tensor variables. We construct approximate systems without tensor variables by using Hurwitz-Radon matrices, so that the systems can be 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. We also prove the convergence of the approximate systems with tensor variables.

主持人：秦玉明

撰写：李学元