Acta mathematica scientia,Series B ›› 2018, Vol. 38 ›› Issue (2): 627-642.doi: 10.1016/S0252-9602(18)30770-7

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DIFFUSION VANISHING LIMIT OF THE NONLINEAR PIPE MAGNETOHYDRODYNAMIC FLOW WITH FIXED VISCOSITY

Zhonglin WU1, Shu WANG2   

  1. 1. College of Mathematics and Statistics, Huanghuai University, Zhumadian 463000, China;
    2. College of Applied Science, Beijing University of Technology, Beijing 100124, China
  • Received:2016-10-08 Revised:2017-10-25 Online:2018-04-25 Published:2018-04-25
  • Supported by:

    The author is supported by Natural Science fund of Henan Province (162300410084), and the Key Research Fund of Henan Province (16A110019), BSFC (1132006), CIT & TCD (20130312).

Abstract:

We establish magnetic diffusion vanishing limit of the nonlinear pipe Magnetohydrodynamic flow by the mathematical validity of the Prandtl boundary layer theory with fixed viscosity. The convergence is verified under various Sobolev norms, including the L(L2) and L(H1) norm.

Key words: Incompressible viscous MHD system, nonmagnetic MHD system, boundary layer, Prandtl theory, corrector

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