Title: On the motion of a slightly compressible liquid

Date: 02/27/2017

Time: 4:10 PM - 5:00 PM

Place: C517 Wells Hall

I would like to go over some recent results on the compressible Euler equations with free boundary. We first provide a new a priori energy estimates which are uniform in the sound speed, which leads to the convergence to the solutions of the incompressible Euler equations. This is a joint work with Hans Lindblad. On the other hand, the energy estimates can be generalized to the compressible water wave problem, i.e., the domain that occupied by the fluid is assumed to be unbounded. We are also able to prove weighted energy estimates for a compressible water wave. Our method requires the detailed analysis of the geometry of the moving boundary.