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arXiv · 2407.02582

An Onsager-type theorem for SQG

Mimi Dai·Vikram Giri·Razvan-Octavian Radu
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Abstract

We construct non-trivial weak solutions $\theta\in C_t^0C_x^{0-}$ to the surface quasi-geostrophic (SQG) equations, which have compact support in time and, thus, violate the conservation of the Hamiltonian. The result is sharp in view of the fact that such a conservation law holds for all weak solutions in the class $C_{t,x}^0 \subset L_{t,x}^3$ (Isett-Vicol, 2015) and resolves the Onsager conjecture for SQG. The construction is achieved by means of a Nash iteration together with the linear decoupling method recently introduced in Giri-Radu (2023).

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Mimi Dai, Vikram Giri, Razvan-Octavian Radu. 2024-07-02. An Onsager-type theorem for SQG. https://arxiv.org/abs/2407.02582

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