Schauder estimate in large scale for compressible planar cavity flows with fast-decaying vorticity

Abstract

In this paper, we study planar compressible cavity flows fast-decaying vorticity and establish a Schauder estimate in large scale. As an application, we obtain an a priori asymptotic growth rate estimate of the cavity, that $s^{\frac{1}{2}-\delta }\lesssim h(s)\lesssim s^{\frac{1}{2}+\delta }$. This is by far the most accurate asymptotic estimate for compressible cavity flows and is probably the first paper that takes vorticity into account in the asymptotic analysis.