报告题目: Global large smooth solutions and relaxation limit of isentropic Euler equations

报告人:   彭跃军 教授 （法国克莱蒙奥弗涅大学）

报告摘要：In this talk, I consider the Cauchy problem for isentropic Euler equations with relaxation close to the isothermal case. I first show that the problem admits a unique smooth solution when either the relaxation time or the initial datum is sufficiently small. Then, in an appropriate time scaling, I establish error estimates of the convergence of the large density of the Euler equations toward the solution of the porous medium equation as the relaxation time tends to zero. Besides energy estimates, a key step to prove these results is a uniform estimate of a quantity related to Darcy's law.

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. Anal.等国际高水平期刊。

报告时间: 2025.5.29(周三) 下午 3:00-4:00

报告地点：教学楼308