On the rigidity from infinity for nonlinear Alfvén waves

2020/01/07 by Mengni Li, Li, Mengni, Pin Yu +1
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions #Primary 35B40 #Secondary 76W05

paper · pdf · doi:10.48550/arxiv.2001.01834

openalex publication_date 2020/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Alfvén waves are fundamental wave phenomena in magnetized plasmas and the dynamics of Alfvén 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 Alfvén 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.

Citations

• Global Well-Posedness of the Incompressible Magnetohydrodynamics
• Global small solutions of 2-D incompressible MHD system

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