A Schauder theory for the Stokes equations in rough domains

Dominic Breit

A Schauder theory for the Stokes equations in rough domains

Analysis of PDEs 2024-01-23 v3

Authors: Dominic Breit

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.

Keywords

stokes equations campanato spaces maximal regularity rough domains pointwise multipliers no-slip boundary

Cite

@article{arxiv.2304.06311,
  title  = {A Schauder theory for the Stokes equations in rough domains},
  author = {Dominic Breit},
  journal= {arXiv preprint arXiv:2304.06311},
  year   = {2024}
}

Comments

To appear in Indiana Univ. Math. J

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