Global solutions of 3D incompressible MHD system with mixed partial dissipation and magnetic diffusion near an equilibrium

This paper focuses on the 3D incompressible magnetohydrodynamic (MHD) equations with mixed partial dissipation and magnetic diffusion. Our main result assesses the global stability of perturbations near the steady solution given by a background magnetic field. The stability problem on the MHD equati...

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2021-01, Vol.377, p.107466, Article 107466
Main Authors: Wu, Jiahong, Zhu, Yi
Format: Article
Language:English
Subjects:
3D magnetohydrodynamic equations
Background magnetic field
Mixed dissipation
Stability
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Summary:This paper focuses on the 3D incompressible magnetohydrodynamic (MHD) equations with mixed partial dissipation and magnetic diffusion. Our main result assesses the global stability of perturbations near the steady solution given by a background magnetic field. The stability problem on the MHD equations with partial or no dissipation has attracted considerable interests recently and there are substantial developments. The new stability result presented here is among the very few stability conclusions currently available for ideal or partially dissipated MHD equations. As a special consequence of the techniques introduced in this paper, we obtain the small data global well-posedness for the 3D incompressible Navier-Stokes equations without vertical dissipation.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2020.107466