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

Xiaoguang You

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

Analysis of PDEs 2024-12-02 v4

Authors: Xiaoguang You

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.

Keywords

2d mhd equations horizontal dissipation horizontal magnetic diffusion local existence uniqueness h^s initial data

Cite

@article{arxiv.2311.09501,
  title  = {Local existence and uniqueness of solutions for the 2D MHD equations with horizontal dissipation and horizontal magnetic diffusion},
  author = {Xiaoguang You},
  journal= {arXiv preprint arXiv:2311.09501},
  year   = {2024}
}

Comments

The result is trivial

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