Local existence and uniqueness of solutions for the 2D MHD equations with horizontal dissipation and horizontal magnetic diffusion

Xiaoguang You

paper

Local existence and uniqueness of solutions for the 2D MHD equations with horizontal dissipation and horizontal magnetic diffusion

arXiv:2311.09501

Abstract

In this paper, we consider the 2D incompressible MHD equations with horizontal dissipation and horizontal magnetic diffusion. We establish local existence and uniqueness of solutions for initial data in $H^{s}$ ( $s \geq 1$ ). The proof relays heavily on new estimates of the nonlinear terms.

The result is trivial