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

Chilin Zhang

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arXiv · 2610.17522

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

Chilin Zhang

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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 $s^{\frac{1}{2}-δ}\lesssim h(s)\lesssim s^{\frac{1}{2}+δ}$. 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.

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Chilin Zhang. 2026-10-13. Schauder estimate in large scale for compressible planar cavity flows with fast-decaying vorticity. https://arxiv.org/abs/2610.17522

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