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arXiv · 2304.06311

A Schauder theory for the Stokes equations in rough domains

Dominic Breit
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Abstract

We consider the steady Stokes equations in a bounded domain with forcing in divergence form supplemented with no-slip boundary conditions. We provide a maximal regularity theory in Campanato spaces (inlcuding $\mathrm{BMO}$ and $C^{0,\alpha}$ for $0<\alpha <1$ as special cases) under minimal assumptions on the regularity of the underlying domain. Our approach is based on pointwise multipliers in Campanto spaces.

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Dominic Breit. 2023-04-13. A Schauder theory for the Stokes equations in rough domains. https://arxiv.org/abs/2304.06311

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