Acta mathematica scientia,Series B ›› 2018, Vol. 38 ›› Issue (3): 898-914.doi: 10.1016/S0252-9602(18)30791-4

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GLOBAL WELLPOSEDNESS OF MAGNETOHYDRODYNAMICS SYSTEM WITH TEMPERATURE-DEPENDENT VISCOSITY

Shibin SU, Xiaokui ZHAO   

  1. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China
  • Received:2017-05-05 Revised:2017-10-20 Online:2018-06-25 Published:2018-06-25
  • Contact: Xiaokui ZHAO E-mail:zhaoxiaokui@126.com
  • Supported by:

    Supported by NNSFC (11271306), the Natural Science Foundation of Fujian Province of China (2015J01023), and the Fundamental Research Funds for the Central Universities of Xiamen University (20720160012).

Abstract:

The initial boundary value problem of the one-dimensional magneto-hydrodynamics system, when the viscosity, thermal conductivity, and magnetic diffusion coefficients are general smooth functions of temperature, is considered in this article. A unique global classical solution is shown to exist uniquely and converge to the constant state as the time tends to infinity under certain assumptions on the initial data and the adiabatic exponent γ. The initial data can be large if γ is sufficiently close to 1.

Key words: MHD system, global well-posedness, temperature-dependent viscosity

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