In this dissertation, we study the motion of a relativistic barotropic fluid with a free boundary. We prove that the system of equations is locally well-posed, and the unique solution has the same regularity as the initial data. We use two methods to achieve the result. The first method is to construct approximate solutions to the equation by mollifying the nonlinear equation directly in the Lagrangian coordinate, and then passing to the limit so that the approximate solutions converge to the exact solution. The second method is to first consider the equation on a linear level, solve the linear equation using Galerkin approximation, and then solve the nonlinear equation by iterating on the solutions to these linear equations and passing to the limit.

Yuxin's advisor is Sijue Wu.

Zoom: https://umich.zoom.us/j/94272426717
passcode: yuxin Speaker(s): Yuxin Wang (UM)