Well-posedness of the compressible boundary layer equations with data in the Gevrey class

TL;DR

This paper establishes local existence and uniqueness of solutions for the compressible boundary layer equations within the Gevrey-2 class, addressing complexities from viscous and thermal layer interactions.

Contribution

It introduces new auxiliary functions and a cancellation mechanism to prove well-posedness of the equations in the Gevrey-2 space, extending classical results.

Findings

Proved local existence and uniqueness of solutions.

Overcame derivative loss via cancellation mechanism.

Handled complex viscous-thermal layer interactions.

Abstract

This paper is devoted to the study of the compressible boundary layer equations in the Gevrey-2 solution space. Compared to the classical Prandtl equation, the additional complexity arises from the strong interaction between viscous layer and thermal layer. By introducing new auxiliary functions and observing the cancellation mechanism to overcome the loss of derivatives, we show the local existence and uniqueness of the solution in the Gevrey-2 space in the tangential variable and Sobolev regularity in the normal variable by using a direct energy method.