Local well-posedness of solutions to the boundary layer equations for 2D compressible flow

Abstract

In this paper, we give a new direct proof by energy method for the local well-posedness of the boundary layer equations for two-dimensional compressible isentropic flow with no-slip boundary condition. It requires less compatibility conditions than the previous result using Nash-Moser-Hörmander iteration scheme and linear energy estimates. It shows that maximum principle works for boundary layer equations so that the weighted L∞ estimates on the lower order terms can be obtained.