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Matematicheskie Zametki, 2016, Volume 99, Issue 6, Pages 803–819
DOI: https://doi.org/10.4213/mzm11161 (Mi mzm11161) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Asymptotic Solutions of a Magnetohydrodynamic System which Describe Smoothed Discontinuities

A. I. Alilluevaab, A. I. Shafarevichcab

a Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region
b Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow
c Lomonosov Moscow State University
Full-text PDF (559 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm11161
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.
Keywords: magnetohydrodynamic system, incompressible fluid, Cauchy problem, free boundary problem, magnetic field, rapidly varying solution, Alfven mode, smoothed discontinuity, Witham equation.
Funding agency Grant number
Russian Foundation for Basic Research 16-31-00664a
14-01-00521a
16-01-00378
Ministry of Education and Science of the Russian Federation 581.2014.1
This work was supported in part by the Russian Foundation for Basic Research under grants 16-31-\abr 00664a, 16-01-00378, and 14-01-00521a and by the program “Leading Scientific Schools” under grant 581.2014.1.
Received: 17.06.2015
Revised: 09.11.2015
English version:
Mathematical Notes, 2016, Volume 99, Issue 6, Pages 795–809
DOI: https://doi.org/10.1134/S0001434616050187
Bibliographic databases:
Document Type: Article
UDC: 517.955+517.957+517.958
Language: Russian
Citation: A. I. Alillueva, A. I. Shafarevich, “Asymptotic Solutions of a Magnetohydrodynamic System which Describe Smoothed Discontinuities”, Mat. Zametki, 99:6 (2016), 803–819; Math. Notes, 99:6 (2016), 795–809
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm11161
  • https://www.mathnet.ru/eng/mzm/v99/i6/p803
    • This publication is cited in the following 2 articles:
    1. A. I. Allilueva, A. I. Shafarevich, “Asymptotic solutions of a system of gas dynamics with low viscosity that describe smoothed discontinuities”, Russ. J. Math. Phys., 27:4 (2020), 411–423  crossref  mathscinet  isi
    2. Allilueva A.I., Shafarevich A.I., “Asymptotic Solutions For Linear and Nonlinear Mhd Systems With a Rapid Jump Near a Surface. Dynamics of the Surface of the Jump and Evolution of the Magnetic Field”, Regul. Chaotic Dyn., 20:6 (2015), 691–700  mathnet  crossref  mathscinet  zmath  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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    References:83
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