Global existence of 3D rotating magnetohydrodynamic equations arising from Earth's fluid core

Jinyi Sun; Weining Wang; Dandan Zhao; Jinyi Sun; Weining Wang; Dandan Zhao

doi:10.3934/nhm.2025003

Networks and Heterogeneous Media

2025, Volume 20, Issue 1: 35-51. doi: 10.3934/nhm.2025003

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Global existence of 3D rotating magnetohydrodynamic equations arising from Earth's fluid core

1.
College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
2.
Gansu Provincial Research Center for Basic Disciplines of Mathematics and Statistics, Lanzhou 730070, China

Received: 27 September 2024 Revised: 10 December 2024 Accepted: 02 January 2025 Published: 09 January 2025

The paper is concerned with the three-dimensional magnetohydrodynamic equations in the rotational framework concerning with fluid flow of Earth's core and the variation of the Earth's magnetic field. By establishing new balances between the regularizing effects arising from viscosity dissipation and magnetic diffusion with the dispersive effects caused by the rotation of the Earth, we obtain the global existence and uniqueness of solutions of the Cauchy problem of the three-dimensional rotating magnetohydrodynamic equations in Besov spaces. Moreover, the spatial analyticity of solutions is verified by means of the Gevrey class approach.
- magnetohydrodynamic equations,
- rotating fluids,
- global solutions,
- Gevrey regularity
Citation: Jinyi Sun, Weining Wang, Dandan Zhao. Global existence of 3D rotating magnetohydrodynamic equations arising from Earth's fluid core[J]. Networks and Heterogeneous Media, 2025, 20(1): 35-51. doi: 10.3934/nhm.2025003

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Abstract

The paper is concerned with the three-dimensional magnetohydrodynamic equations in the rotational framework concerning with fluid flow of Earth's core and the variation of the Earth's magnetic field. By establishing new balances between the regularizing effects arising from viscosity dissipation and magnetic diffusion with the dispersive effects caused by the rotation of the Earth, we obtain the global existence and uniqueness of solutions of the Cauchy problem of the three-dimensional rotating magnetohydrodynamic equations in Besov spaces. Moreover, the spatial analyticity of solutions is verified by means of the Gevrey class approach.

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