Non-unique weak solutions of forced SQG

Mimi Dai; Qirui Peng

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arXiv · 2310.13537

Non-unique weak solutions of forced SQG

Mimi Dai·Qirui Peng

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Abstract

We construct non-unique weak solutions $\theta\in C_t^0C_x^{0-}$ for forced surface quasi-geostrophic (SQG) equation. This is achieved through a convex integration scheme adapted to the sum-difference system of two distinct solutions. Without external forcing, non-unique weak solutions $\theta$ in space $C_t^0C_x^{\alpha}$ with $\alpha<-\frac15$ were constructed by Buckmaster, Shkoller and Vicol, and Isett and Ma.

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Mimi Dai, Qirui Peng. 2023-10-20. Non-unique weak solutions of forced SQG. https://arxiv.org/abs/2310.13537

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