科院数学与系统科学研究院
数学研究所
偏微分方程研讨班
报告人： Dr. Chenyun Luo(Vanderbilt University, USA)
题 目：Recent developments on free-boundary fluid models
时 间：2019.05.31（星期五）, 10:30-11:30
地 点：数学院南楼N913室
摘 要：In this talk, we survey some recent results on the motion of a liquid with free surface boundary. Specifically, we will cover: 1. Local well-posedness for the motion of a compressible, self-gravitating liquid. We do this by solving a tangentially-smoothed version of the Euler equations which satisfies uniform energy estimate as the smoothing parameter goes to zero. 2. Incompressible limit for the motion of a compressible liquid with or without surface tension. We prove that the motion of a compressible free-boundary liquid with large sound speed can be ``well-approximated' by that of an incompressible free-boundary liquid. This requires a dedicate energy estimate that is uniform as the sound speed goes to infinity. 3. Rough solutions for incompressible free-boundary MHD equations. We employ the method for Euler equations to study the solution for free-boundary incompressible MHD equations in Sobolev spaces with low regularity.
