Well-posedness of the compressible boundary layer equations with analytic initial data

TL;DR

This paper proves the local well-posedness of the compressible boundary layer equations with analytic initial data, using Littlewood-Paley theory to establish a priori estimates for solutions.

Contribution

It establishes the local existence and uniqueness of solutions for the compressible boundary layer equations with analytic tangential data, a novel result in this context.

Findings

Proved local well-posedness of the equations.

Established a priori estimates using Littlewood-Paley theory.

Demonstrated uniqueness of solutions in the analytic setting.

Abstract

We study the well-posedness of the compressible boundary layer equations with data being analytic in the tangential variable of the boundary. The compressible boundary layer equations, a nonlinear coupled system of degenerate parabolic equations and an elliptic equation, describe the behavior of thermal layer and viscous layer in the small viscosity and heat conductivity limit, for the two-dimensional compressible viscous flow with heat conduction with nonslip and zero heat flux boundary conditions. We use the Littlewood-Paley theory to establish the a priori estimates for solutions of this compressible boundary layer problem, and obtain the local existence and uniqueness of the solution in the space of analytic in the tangential variable and Sobolev in the normal variable.