Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Speaker:
Dr. Chenyun Luo,Vanderbilt University, USA
Inviter:
Title:
Recent developments on free-boundary fluid models
Time & Venue:
2019.5.31 10:30-11:30 N913
Abstract:
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.