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.

中文翻译：

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SQG 方程的非唯一性和紧致性失败的直接方法

我们给出了第一个在 [3] 中显示的表面拟地转方程 (SQG) 的弱解的非唯一性的替代证明。我们的方法直接在标量场的水平上进行。此外，我们证明了每个具有紧支持的光滑标量场都可以实现为 SQG 解的弱极限。