Tristan Buckmaster, Steve Shkoller, Vlad Vicol
Published 2016-10-03Version 1
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.
Weak solutions, renormalized solutions and enstrophy defects in 2D turbulence
Segregated configurations involving the square root of the laplacian and their free boundaries
Multiple solutions of nonlinear equations involving the square root of the Laplacian
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