Low Mach number limit of Navier-Stokes equations in bounded domains
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：欧耀彬（中国人民大学）
：2022-07-13 15:00
：腾讯会议ID：592-310-704（无密码）
报告人：欧耀彬（中国人民大学）
时 间：7月13日下午15:00
地 点：腾讯会议ID：592-310-704（无密码）
内容摘要:
In this talk, I first discuss the incompressible limit of strong solutions to the isentropic compressible Navier-Stokes equations with ill-prepared initial data and slip boundary condition in a three-dimensional bounded domain, which is a joint work with Lu Yang. Previous results only deal with the cases of the weak solutions or the cases without solid boundary, where the uniform estimates are much easier to be shown. We propose a new weighted energy functional to establish the uniform estimates, in particular for the time derivatives and the high-order spatial derivatives. The estimates of highest order spatial derivatives of fast variables are crucial for the uniform bounds of solutions. The incompressible limit is shown by applying the Helmholtz decomposition, the weak convergence of the velocity and the strong convergence of its divergence-free component. Next, I discuss related results on the low Mach number limit of non-isentropic Navier-Stokes equations, in particular for the case of well-prepared initial data and/or Dirichlet boundary condition.
个人简介：
欧耀彬，博士，中国人民大学数学系教授、博士生导师。2001年、2004年本科和硕士毕业于中山大学，2008年博士毕业于香港中文大学，北京应用物理与计算数学研究所和西班牙巴斯克应用数学中心博士后，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，包括解的适定性问题、渐近极限问题等。论文发表在JMPA、SIMA、ANIHP等重要刊物。
联系人：王焰金
