Global well‐posedness of 3D incompressible inhomogeneous magnetohydrodynamic equations

In this paper, we investigate the 3D inhomogeneous incompressible magnetohydrodynamic (MHD) system. By the assumption of the smallness of initial velocity and magnetic fluids in the critical Besov space, the local and global well‐posedness of 3D inhomogeneous incompressible equations is obtained. It...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2023-01, Vol.46 (2), p.2906-2940
Main Authors: Huang, Tian, Qian, Chenyin
Format: Article
Language:English
Subjects:
Besov spaces
Fluid flow
Function space
Incompressible flow
inhomogeneous MHD equations
Littlewood–Paley theory
Magnetic fluids
Magnetohydrodynamic equations
Magnetohydrodynamics
Mathematical analysis
well‐posedness
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Summary:In this paper, we investigate the 3D inhomogeneous incompressible magnetohydrodynamic (MHD) system. By the assumption of the smallness of initial velocity and magnetic fluids in the critical Besov space, the local and global well‐posedness of 3D inhomogeneous incompressible equations is obtained. It improves some previous results of MHD equations by generalizing the range of exponent p$$ p $$ in Besov spaces B˙p,13/p−1$$ {\dot{B}}_{p,1}^{3/p-1} $$ with 1
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.8679