Local well-posedness of the vacuum free boundary of 3-D compressible Navier-Stokes equations

Abstract

In this paper, we consider the 3-D motion of viscous gas with the vacuum free boundary. We use the conormal derivative to establish local well-posedness of this system. One of important advantages in the paper is that we do not need any strong compatibility conditions on the initial data in terms of the acceleration.

31 pages