The local well-posedness of analytic solution to the boundary layer system for compressible flow in three dimensions

Abstract

In this paper, we consider three dimensional boundary layer equations for compressible isentropic flow with no-slip boundary condition. The local well-posedness of the compressible boundary layer system is established when the initial datum is real-analytic in the tangential direction and has Sobolev regularity in the normal direction. The proof is based on the introduction of a change of variables to eliminate the linear growth in normal direction and subtle energy estimates with algebraic weights.