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Vanishing vertical limit of the incompressible combined viscosity and magnetic diffusion magnetohydrodynamic system
Author(s) -
Wang Na,
Wang Shu
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4950
Subject(s) - magnetohydrodynamic drive , viscosity , mathematics , magnetohydrodynamics , compressibility , diffusion , mathematical analysis , limit (mathematics) , boundary layer , magnetic field , physics , mechanics , thermodynamics , quantum mechanics
In this paper, we consider the incompressible combined viscosity and magnetic diffusion magnetohydrodynamic system with Dirichlet boundary condition in a half space of R 3 . We establish the asymptotic expansions of this system by multiscale analysis and obtain the horizontal alone viscosity and magnetic diffusion magnetohydrodynamic equations and the boundary layer equations. And then we study the well‐posedness of the 2 equations. At last, we get the vanishing limit when the vertical viscosity and magnetic diffusion coefficient tends to zero.