English

Liouville-type theorem for steady helically symmetric MHD system in $\mathbb{R}^{3}$

Analysis of PDEs 2024-05-21 v1

Abstract

We show that any bounded smooth helically symmetric solution (\Bu,\Bh)(\Bu, \Bh) in R3\mathbb{R}^3 must be constant vectors. This is an extension of previous result \cite[Theorem 1.1]{HWXAHE} from Navier-Stokes system to MHD system. The proof relies on establishing a Saint-Venant type estimate to characterize the growth of Dirichlet integral of nontrivial solutions.

Keywords

Cite

@article{arxiv.2405.11521,
  title  = {Liouville-type theorem for steady helically symmetric MHD system in $\mathbb{R}^{3}$},
  author = {Jingwen Han},
  journal= {arXiv preprint arXiv:2405.11521},
  year   = {2024}
}