Abstract:In this paper, we prove that weak solutions to the 2D viscous and resistive magnetohydrodynamic (MHD) equations are non-unique in $L^2_t L^p(\mathbb{R}^2) \cap L^1_t W^{1,p}(\mathbb{R}^2)$ for given any $1\le p<\infty$, showing the sharpness of the Ladyzhenskaya--Prodi--Serrin condition at the endpoint $(2,\infty)$ and the solutions live on the borderline of the Beale--Kato--Majda criterion. To the best of our knowledge, this is the first non-uniqueness result for the 2D viscous and resistive MHD system. As byproducts, we also obtain non-uniqueness for the Navier--Stokes equations in $L^2_t L^p$ with $1\le p<\infty$, and for the MHD system with large $\mathrm{BMO}^{-1}$ initial data.
| Subjects: | Analysis of PDEs (math.AP) |
| Cite as: | arXiv:2605.25097 [math.AP] |
| (or arXiv:2605.25097v1 [math.AP] for this version) | |
| https://doi.org/10.48550/arXiv.2605.25097 arXiv-issued DOI via DataCite (pending registration) |
From: Yao Nie [view email]
[v1]
Sun, 24 May 2026 14:18:28 UTC (27 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。