Qirui Peng : Non-unique weak solutions of forced SQG

Posted by Christof Sparber , part of the Analysis and Applied Mathematics Seminar.

At

March 11, 2024, 4 p.m.

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636 SEO

Abstract

We construct non-unique weak solutions $\theta \in C^0_t C^{0-}_x$ for forced surface quasi-geostrophic (SQG) equations. 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 $C^0_t C^\alpha_x$ with $\alpha < -1/5$ were constructed by Buckmaster, Shkoller and Vicol (2019) and Isett and Ma (2021).