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arXiv · 2307.06587

Weak solutions to the Hall-MHD equations whose singular sets in time have Hausdorff dimension strictly less than 1

Yi Peng·Huaqiao Wang
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Abstract

In this paper, we focus on the three-dimensional hyper viscous and resistive Hall-MHD equations on the torus, where the viscous and resistive exponent $α\in [ρ, 5/4)$ with a fixed constant $ρ\in (1,5/4)$. We prove the non-uniqueness of a class of weak solutions to the Hall-MHD equations, which have bounded kinetic energy and are smooth in time outside a set whose Hausdorff dimension strictly less than 1. The proof is based on the construction of the non-Leray-Hopf weak solutions via a convex integration scheme.

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Yi Peng, Huaqiao Wang. 2023-07-13. Weak solutions to the Hall-MHD equations whose singular sets in time have Hausdorff dimension strictly less than 1. https://arxiv.org/abs/2307.06587

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