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Global Well-Posedness for the 3D Axisymmetric Hall-MHD System with Horizontal Dissipation
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Global Well-Posedness for the 3D Axisymmetric Hall-MHD System with Horizontal Dissipation
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Journal Article
Global Well-Posedness for the 3D Axisymmetric Hall-MHD System with Horizontal Dissipation
2022
Overview
Studied in this paper is the Cauchy problem for the 3D incompressible Hall-MHD system with horizontal dissipation. It is shown that if the initial data is axisymmetric and the swirl component of the velocity and the magnetic vorticity are trivial, such a system is globally well-posed for the large initial data. The key is to take full advantage of the structure of the Hall-MHD system in axisymmetric case to overcome the main difficulty due to the absence of vertical dissipation.
Publisher
Springer Netherlands,Springer Nature B.V
