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arXiv · 2305.18509

The $L^3$-based strong Onsager theorem

Vikram Giri·Hyunju Kwon·Matthew Novack
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Abstract

In this work, we prove the $L^3$-based strong Onsager conjecture for the three-dimensional Euler equations. Our main theorem states that there exist weak solutions which dissipate the total kinetic energy, satisfy the local energy inequality, and belong to $C^0_t (W^{\frac 13-, 3} \cap L^{\infty-})$. More precisely, for every $\beta<\frac 13$, we can construct such solutions in the space $C^0_t ( B^{\beta}_{3,\infty} \cap L^{\frac{1}{1-3\beta}} )$.

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Vikram Giri, Hyunju Kwon, Matthew Novack. 2023-05-29. The $L^3$-based strong Onsager theorem. https://arxiv.org/abs/2305.18509

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