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

Fuente: arXiv
Saved in:
Bibliographic Details
Main Author: Han, Jingwen
Format: Preprint
Published: 2024
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866910452863205376
author Han, Jingwen
author_facet Han, Jingwen
contents We show that any bounded smooth helically symmetric solution $(\Bu, \Bh)$ in $\mathbb{R}^3$ 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.
format Preprint
id arxiv_https___arxiv_org_abs_2405_11521
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Liouville-type theorem for steady helically symmetric MHD system in $\mathbb{R}^{3}$
Han, Jingwen
Analysis of PDEs
We show that any bounded smooth helically symmetric solution $(\Bu, \Bh)$ in $\mathbb{R}^3$ 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.
title Liouville-type theorem for steady helically symmetric MHD system in $\mathbb{R}^{3}$
topic Analysis of PDEs
url https://arxiv.org/abs/2405.11521