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arXiv · 2007.03078

A direct approach to nonuniqueness and failure of compactness for the SQG equation

Philip Isett·Andrew Ma
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Abstract

We give an alternative proof of the nonuniqueness of weak solutions to the surface quasigeostrophic equation (SQG) first shown in [Buckmaster-Shkoller-Vicol, '16]. Our approach proceeds directly at the level of the scalar field. Furthermore, we prove that every smooth scalar field with compact support that conserves the integral can be realized as a weak limit of solutions to SQG.

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Philip Isett, Andrew Ma. 2020-07-06. A direct approach to nonuniqueness and failure of compactness for the SQG equation. https://doi.org/10.1088/1361-6544/abe732

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