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Nonuniqueness of weak solutions to the SQG equation

PDE and Applied Math Seminar

Speaker: Steve Shkoller, UC Davis
Location: 1147 MSB
Start time: Fri, Oct 7 2016, 4:10PM

In this talk, we prove that weak solutions of the inviscid surface quasi-geostrophic (SQG) equation are not unique, thereby answering an open problem posed by De Lellis and Szekelihidi. 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. Our proof is based on a reformulation of the SQG equation combined with convex integration. This is joint work with T. Buckmaster and V. Vicol.