On the rigidity from infinity for nonlinear Alfv\'en waves

Mengni Li; Pin Yu

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arXiv · 2001.01834

On the rigidity from infinity for nonlinear Alfv\'en waves

Mengni Li·Pin Yu

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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.

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Mengni Li, Pin Yu. 2020-01-07. On the rigidity from infinity for nonlinear Alfv\'en waves. https://arxiv.org/abs/2001.01834

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