On the rigidity from infinity for nonlinear Alfv\'en waves
Analysis of PDEs
2020-01-08 v1
Abstract
The Alfv\'en waves are fundamental wave phenomena in magnetized plasmas and the dynamics of Alfv\'en waves are governed by a system of nonlinear partial differential equations called the MHD system. In this paper, we study the rigidity aspect of the scattering problem for the MHD equations: We prove that the Alfv\'en waves must vanish if their scattering fields vanish at infinities. The proof is based on a careful study of the null structure and a family of weighted energy estimates.
Keywords
Cite
@article{arxiv.2001.01834,
title = {On the rigidity from infinity for nonlinear Alfv\'en waves},
author = {Mengni Li and Pin Yu},
journal= {arXiv preprint arXiv:2001.01834},
year = {2020}
}
Comments
34 pages, 6 figures