Partial boundary regularity for the Navier-Stokes equations in irregular domains
Abstract
We prove partial regularity of suitable weak solutions to the Navier--Stokes equations at the boundary in irregular domains. In particular, we provide a criterion which yields continuity of the velocity field in a boundary point and obtain solutions which are continuous in a.a. boundary boundary point (their existence is a consequence of a new maximal regularity result for the Stokes equations in domains with minimal regularity). We suppose that we have a Lipschitz boundary with locally small Lipschitz constant which belongs to the fractional Sobolev space for some . The same result was previously only known under the much stronger assumption of a -boundary.
Cite
@article{arxiv.2208.00415,
title = {Partial boundary regularity for the Navier-Stokes equations in irregular domains},
author = {Dominic Breit},
journal= {arXiv preprint arXiv:2208.00415},
year = {2022}
}
Comments
We added the proof of the maximal regularity theory for the unsteady Stokes system in irregular domains. A variant of it was previously included in arXiv:2207.14159 but has been removed in the revised version. arXiv admin note: text overlap with arXiv:2207.14159