Geodesic
Asymptotic Solutions of a Magnetohydrodynamic System which Describe Smoothed Discontinuities
Matematičeskie zametki, Tome 99 (2016) no. 6, pp. 803-819

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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 $1$.
Keywords: magnetohydrodynamic system, Cauchy problem, free boundary problem, magnetic field, rapidly varying solution, Alfven mode, smoothed discontinuity, Witham equation.
Mots-clés : incompressible fluid 
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     author = {A. I. Alillueva and A. I. Shafarevich},
     title = {Asymptotic {Solutions} of a {Magnetohydrodynamic} {System} which {Describe} {Smoothed} {Discontinuities}},
     journal = {Matemati\v{c}eskie zametki},
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     publisher = {mathdoc},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_99_6_a0/}
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A. I. Alillueva; A. I. Shafarevich. Asymptotic Solutions of a Magnetohydrodynamic System which Describe Smoothed Discontinuities. Matematičeskie zametki, Tome 99 (2016) no. 6, pp. 803-819. http://geodesic.mathdoc.fr/item/MZM_2016_99_6_a0/