The local well-posedness of the three-dimensional compressible isentropic boundary layer equations

The Prandtl equations governing the boundary layer for incompressible flows are extensively studied in different contexts.The mathematical study of boundary layers for compressible flows remains relatively limited.In particular, in the three-dimensional setting, there are few results for boundary layer problems in either incompressible or compressible flows.In this paper, we consider the three-dimensional boundary layer equations for compressible isentropic flows with no-slip boundary conditions.Under the assumption that the initial data is analytic in the tangential variables and has Sobolev regularity in the normal direction, we establish the local well-posedness of the system using direct energy estimates.