publication . Preprint . 2015

Global solvability, non-resistive limit and magnetic boundary layer of the compressible heat-conductive MHD equations

Zhang, Jianwen; Zhao, Xiaokui;
Open Access English
  • Published: 13 Oct 2015
Abstract
In general, the resistivity is inversely proportional to the electrical conductivity, and is usually taken to be zero when the conducting fluid is of extremely high conductivity (e.g., ideal conductors). In this paper, we first establish the global well-posedness of strong solution to an initial-boundary value problem of the one-dimensional compressible, viscous, heat-conductive, non-resistive MHD equations with general heat-conductivity coefficient and large data. Then, the non-resistive limit is justified and the convergence rates are obtained, provided the heat-conductivity satisfies some growth condition. Finally, we discuss the thickness of the magnetic bou...
Subjects
arXiv: Physics::Fluid Dynamics
free text keywords: Mathematics - Analysis of PDEs, 35B45, 35L65, 35Q60, 76N10
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23 references, page 1 of 2

[1] H. Alfv´en, Existence of electromagnetic-hydrodynamic waves. Nature 150 (1942), 405-406.

[2] A. A. Amosov, A. A. Zlotnik, A difference scheme on a non-uniform mesh for the equations of onedimensional magneticgasdynamics. U.S.S.R. Compu. Maths. Math. Phys., 29(2) (1990), 129-139.

[3] J.A. Bittencourt, Fundamentals of Plasma Physics 3rd. New York: Spinger-Verlag, 2004.

[4] T.J.M. Boyd, J.J. Sanderson, The Physics of Plasmas. Cambridge: Cambridge Univ. Press, 2003.

[5] H. Cabannes, Theoretical Magnetofluiddynamics. New York: Academic Press, 1970.

[6] G.-Q. Chen, D. Wang, Global solutions of nonlinear magnetohydrodynamics with large initial data. J. Differential Equations, 182 (2002), 344-376.

[7] S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability. Oxford: Oxford Univ. Press, 1961.

[8] G.-Q. Chen and D. Wang, Existence and continuous dependence of large solutions for the magnetohydrodynamic equations. Z. Angew. Math. Phys., 54 (2003), 608-632.

[9] J. Fan, Y. Hu, Global strong solutions to the 1-D compressible magnetohydrodynamic equations with zero resistivity. J. Math. Phys., 56 (2015), 023101.

[10] J.P. Freidberg, Ideal Magnetohydrodynamic Theory of Magnetic Fusion Systems. Rev. Modern Physics Vol. 54, No 3, The American Physical Society, 1982.

[11] H. Frid, V. V. Shelukhn, Boundary layer for the Navier-Stokes equations of compressible fluids. Commun. Math. Phys., 208 (1999), 309-330. [OpenAIRE]

[13] R.D. Hazeltine, J.D. Meiss, Plasma Confinement. Addison-Wesley, 1992.

[14] D.A. Iskenderova, An initial-boundary value problem for magnetogasdynamic equations with degenerate density. Differetial Eqns., 36 (2000), 847-856.

[15] S. Jiang, J. W. Zhang, Boundary layers for the Navier-Stokes equations of compressible heatconducting flows with cylindrical symmetry. SIAM J. Math. Anal., 41 (2009), 237-268.

[24] F. Lin, T. Zhang, Global small solutions to a complex fluid model in three dimensional. Arch. Ration. Mech. Anal., 216 (2015), 905-920.

23 references, page 1 of 2
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