Local well-posedness for the motion of a compressible self-gravitating liquid with free surface boundary
Dr Luo Chenyun
Date & Time
25 Jun 2019 (Tue) | 04:00 PM - 05:00 PM
Venue
B5-309, Blue Zone, Floor 5, Yeung Kin Man Academic Building (AC1), CityU
Abstract
We establish the local well-posedness for the free boundary problem for the compressible Euler equations describing the motion of liquid under the influence of Newtonian self-gravity. We do this by solving a tangentially-smoothed version of Euler’s equations in Lagrangian coordinates which satisfies uniform energy estimates as the smoothing parameter goes to zero. The main technical tools are delicate energy estimates and optimal elliptic estimates in terms of boundary regularity, for the Dirichlet problem and Green’s function.