Local Well-Posedness of Prandtl Equations for Compressible Flow in Two Space Variables

Abstract

In this paper, we consider the local well-posedness of the Prandtl boundary layer equations that describe the behavior of the boundary layer in the small viscosity limit of the compressible isentropic Navier--Stokes equations with nonslip boundary condition. Under the strictly monotonic assumption on the tangential velocity in the normal variable, we apply the Nash--Moser--Hörmander iteration scheme and further develop the energy method introduced in [R. Alexander et al., J. Amer. Math. Soc., DOI:S0894-0347(2014)00813-4] to obtain the well-posedness of the equations locally in time.