报告人：欧耀彬 教授（中国人民大学）

时 间：2021年06月23日14：30 -15：20

地 点：腾讯会议ID：765 310 292

报告摘要：In this talk, we discuss the low Mach and Froude number limit for the all-time classical solution of a fluid-vacuum free boundary problem of one-dimensional compressible Navier-Stokes equations. No smallness of initial data for the existence of all-time solutions are supposed. The uniform estimates of solutions with respect to the Mach number and the Froude number are established for all the time, in particular for high order derivatives of the pressure, which is a novelty in contrast to previous results. The cases of "ill-prepared" initial data and "well-prepared" initial data are both discussed. It is interesting to see, either both the Mach number and the Froude number vanish, or the time goes to infinity, the limiting functions are the same, that is, the steady state.  At the same time, we also establish the all-time existence of the classical solution with sharp convergent rates to the steady state, while previous results are only concerned with the weak or strong solutions.

报告人简介：欧耀彬，中国人民大学教授，于2008年在香港中文大学获博士学位，曾入选教育部“新世纪优秀人才支持计划”。主要研究方向为流体力学中的偏微分方程理论，在J. Math. Pure. Appl.、SIAM J. Math. Anal.、ANIHP (C)Anal. Non.、J. Diff. Eqns.等国际杂志发表论文20余篇，主持过多项国家级项目和省部级科研项目。