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

2023/07/13 by Peng, Yi, Wang, Huaqiao · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2307.06587

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∈ [ρ, 5/4) with a fixed constant ρ∈ (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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