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 boundary layer in the small viscosity limit of the compressible isentropic Navier-Stokes equations with non-slip 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 [1] to obtain the well-posedness of the equations locally in time.

28 pages

References in corpus (3)

• A note on the Prandtl boundary layers
• Local-in-Time Existence and Uniqueness of Solutions to the Prandtl Equations by Energy Methods
• Well-posedness of The Prandtl Equation in Sobolev Spaces