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Asymptotic solutions of a magnetohydrodynamic system which describe smoothed discontinuities

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Abstract

Asymptotic solutions of a nonlinear magnetohydrodynamic system rapidly varying near moving surfaces are described. It is shown that the motion of jump surfaces is determined from a free boundary problem, while the main part of the asymptotics satisfies a system of equations on the moving surface. In the “nondegenerate” case, this system turns out to be linear, while, under the additional condition that the normal component of the magnetic field vanishes, it becomes nonlinear. In the latter case, the small magnetic field instantaneously increases to a value of order 1.

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Authors and Affiliations

  1. Ishlinskii Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia

    A. I. Allilueva & A. I. Shafarevich

  2. Moscow Institute of Physics and Technology (State University), Dolgoprudnyi, Moscovskaya Oblast, Russia

    A. I. Allilueva & A. I. Shafarevich

  3. National Research Center “Kurchatov Institute,”, Moscow, Russia

    A. I. Allilueva & A. I. Shafarevich

  4. Lomonosov Moscow State University, Moscow, Russia

    A. I. Shafarevich

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  1. A. I. Allilueva
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  2. A. I. Shafarevich
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Correspondence to A. I. Allilueva.

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Original Russian Text © A. I. Allilueva, A. I. Shafarevich, 2016, published in Matematicheskie Zametki, 2016, Vol. 99, No. 6, pp. 803–819.

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Allilueva, A.I., Shafarevich, A.I. Asymptotic solutions of a magnetohydrodynamic system which describe smoothed discontinuities. Math Notes 99, 795–809 (2016). https://doi.org/10.1134/S0001434616050187

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  • DOI: https://doi.org/10.1134/S0001434616050187

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