Global well-posedness of slightly supercritical active scalar equations
Analysis of PDEs
2016-01-20 v1
Abstract
The paper is devoted to the study of slightly supercritical active scalars with nonlocal diffusion. We prove global regularity for the surface quasi-geostrophic (SQG) and Burgers equations, when the diffusion term is supercritical by a symbol with roughly logarithmic behavior at infinity. We show that the result is sharp for the Burgers equation. We also prove global regularity for a slightly supercritical two-dimensional Euler equation. Our main tool is a nonlocal maximum principle which controls a certain modulus of continuity of the solutions.
Keywords
Cite
@article{arxiv.1203.6302,
title = {Global well-posedness of slightly supercritical active scalar equations},
author = {Michael Dabkowski and Alexander Kiselev and Luis Silvestre and Vlad Vicol},
journal= {arXiv preprint arXiv:1203.6302},
year = {2016}
}