Global existence and uniqueness of weak solutions for the MHD equations with large $L^3$-initial values
Analysis of PDEs
2026-02-10 v1
Abstract
This paper is concerned with the weak solution theory for the MHD system with large -initial data. Due to the fact that the natural boundary condition on the magnetic field is the slip boundary condition, the Leray-Schauder fixed-point theorem, which have used to investigate the weak solution theory of the Navier-Stokes system, becomes invalid. To address such difficulty, we will invoke the Leray's approximation technique and the perturbation theory to seek a global weak solution to the Cauchy problem for MHD equations with large -initial data. Our strategy provides a simple alternative (self-contained) proof of weak -solution theory of incompressible Navier-Stokes system. Moreover, this weak solution is unique under some restrictions.
Cite
@article{arxiv.2602.06979,
title = {Global existence and uniqueness of weak solutions for the MHD equations with large $L^3$-initial values},
author = {Baishun Lai and Ge Tang and Ziying Xu},
journal= {arXiv preprint arXiv:2602.06979},
year = {2026}
}