On the global existence to Hall-MHD system

Lvqiao Liu

doi:10.3934/dcdsb.2022044

Article Contents

2022, Volume 27, Issue 12: 7301-7314. Doi: 10.3934/dcdsb.2022044

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On the global existence to Hall-MHD system

Lvqiao Liu

Department of Mathematics and Statistics, Anhui Normal University, Wuhu, 241001, China

Received: December 31, 2020

Revised: December 31, 2021

Early access: March 2022

Published: December 2022

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Abstract

This paper investigates the well-posedness of Hall-magnetohydrodynamics system. By using a new current function $ J = \nabla\times B $ as an additional unknown. The mild solution of Hall-MHD exists globally in the nonhomogeneous Lei-Lin space setting provided that the initial data satisfies $ \|u_{0}\|_{\mathcal{X}^{-1} }+\|B_{0}\|_{ \mathcal{X}^{-1}}+\|J_{0}\|_{ \mathcal{X}^{-1}}<\min \{\frac{\mu }{2}, \frac{\nu }{2}\}. $

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Mathematics Subject Classification: Primary: 35A01, 35J47; Secondary: 35Q35.

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