Well-posedness of the compressible boundary layer equations with data in the Gevrey class
Analysis of PDEs
2026-04-20 v1
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.
Keywords
Cite
@article{arxiv.2604.15878,
title = {Well-posedness of the compressible boundary layer equations with data in the Gevrey class},
author = {Ya-Guang Wang and Yi-Lei Zhao},
journal= {arXiv preprint arXiv:2604.15878},
year = {2026}
}