@article{Yuan2026, 
author = {Shaoliang Yuan},
title = {Weak solutions for two-dimensional magnetohydrodynamics equations with partial dissipation and magnetic diffusion},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {3},
pages = {8832-8841},
keywords = {MHD equations, local existence, uniqueness, partial dissipation and magnetic diffusion},
url = {https://www.sciopen.com/article/10.3934/math.2026363},
doi = {10.3934/math.2026363},
abstract = {In this article, we study the existence of weak solutions to two-dimensional incompressible magnetohydrodynamics (MHD) equations. For the case with only magnetic diffusion, the global existence of solutions in        L    ∞    (  0  ,  ∞  ;      H    1    ) was established by Kozono, whereas the existence of        L    ∞    (  0  ,  ∞  ;      H    1    ) solutions for the case with only dissipation is totally unknown. The purpose here is to consider the mixed case, that is, a system with partial dissipation and partial magnetic diffusion. We show that there exists a unique local solution with initial data in        H    1   space.}
}