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Validity of boundary layer theory for the 3D plane‐parallel nonhomogeneous electrically conducting flows
Author(s) -
Guo Lianhong,
Ji Zhijun
Publication year - 2021
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.7314
Subject(s) - magnetohydrodynamic drive , magnetohydrodynamics , mathematics , sobolev space , magnetic field , compressibility , boundary layer , mathematical analysis , boundary value problem , plane (geometry) , rate of convergence , mechanics , classical mechanics , geometry , physics , computer science , computer network , channel (broadcasting) , quantum mechanics
In this paper, we validate the boundary layer expansion for a family of plane‐parallel flows to nonhomogeneous incompressible magnetohydrodynamic equations with no‐slip boundary conditions imposed on velocity field and perfectly conducting conditions on magnetic field. The convergence rate is established in Sobolev sense. We extend the result of Navier–Stokes system to the case of MHD equations and also investigate the stabilizing effect of the magnetic field by considering the uniform magnetic field.