A direct approach to nonuniqueness and failure of compactness for the SQG equation
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math.AP
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approachequationfieldnonuniquenessscalarsolutionsweakalternative
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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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