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

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We give an alternative proof of the nonuniqueness of weak solutions to the surface quasigeostrophic equation (SQG) first shown in [3]. Our approach proceeds directly at the level of the… Click to show full abstract

We give an alternative proof of the nonuniqueness of weak solutions to the surface quasigeostrophic equation (SQG) first shown in [3]. 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.

Keywords: approach nonuniqueness; nonuniqueness failure; direct approach; approach; failure compactness; equation

Journal Title: Nonlinearity
Year Published: 2020

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