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

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 $s^{\frac{1}{2}-δ}\lesssim h(s)\lesssim s^{\frac{1}{2}+δ}$. This is by far t