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In this paper, we consider the local well-posedness of the Prandtl boundarylayer equations that describe the behavior of boundary layer in the smallviscosity limit of the compressible isentropic Navier-Stokes equations withnon-slip boundary condition. Under the strictly monotonic assumption on thetangential velocity in the normal variable, we apply theNash-Moser-H\"{o}rmander iteration scheme and further develop the energy methodintroduced in [1] to obtain the well-posedness of the equations locally intime.

Local well-posedness of Prandtl equations for compressible flow in two space variables