Nonuniqueness of weak solutions to the SQG equation
Analysis of PDEs
2016-10-04 v1
Abstract
We prove that weak solutions of the inviscid SQG equations are not unique, thereby answering Open Problem 11 in the survey arXiv:1111.2700 by De Lellis and Sz\'ekelyhidi Jr. Moreover, we also show that weak solutions of the dissipative SQG equation are not unique, even if the fractional dissipation is stronger than the square root of the Laplacian.
Cite
@article{arxiv.1610.00676,
title = {Nonuniqueness of weak solutions to the SQG equation},
author = {Tristan Buckmaster and Steve Shkoller and Vlad Vicol},
journal= {arXiv preprint arXiv:1610.00676},
year = {2016}
}
Comments
49 pages