English

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

R2 v1 2026-06-23T13:04:31.039Z