Holder Regularity up to the Boundary for Critical SQG on Bounded Domains
Analysis of PDEs
2020-02-14 v2
Abstract
We consider the dissipative SQG equation in bounded domains, first introduced by Constantin and Ignatova in 2016. We show global Holder regularity up to the boundary of the solution, with a method based on the De Giorgi techniques. The boundary introduces several difficulties. In particular, the Dirichlet Laplacian is not translation invariant near the boundary, which leads to complications involving the Riesz transform.
Keywords
Cite
@article{arxiv.1906.00251,
title = {Holder Regularity up to the Boundary for Critical SQG on Bounded Domains},
author = {Logan Stokols and Alexis Vasseur},
journal= {arXiv preprint arXiv:1906.00251},
year = {2020}
}
Comments
added proof of global existence, made several expositional changes based on referee report