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 in 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}
}