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Matematicheskie Zametki, 2017, Volume 102, Issue 6, Pages 807–815
DOI: https://doi.org/10.4213/mzm11735 (Mi mzm11735) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Localized Asymptotic Solutions of the Linearized System of Magnetic Hydrodynamics

A. I. Alliluevaabc, A. I. Shafarevichabcd

a Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow
b Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region
c National Research Centre "Kurchatov Institute", Moscow
d Lomonosov Moscow State University
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DOI: https://doi.org/10.4213/mzm11735
Abstract: We describe the asymptotic solutions of the Cauchy problem for the linearized system of equations of magnetic hydrodynamics with initial conditions localized near one point. It is shown that the structure of such solutions depends on whether the external magnetic field vanishes or not at this point. We discuss whether it is possible for the asymptotic solution to increase with time.
Keywords: equation of magnetic hydrodynamics, localized asymptotic solutions.
Funding agency Grant number
Russian Science Foundation 16-11-10282
This work was supported by the Russian Science Foundation under grant 16-11-10282.
Received: 07.06.2017
English version:
Mathematical Notes, 2017, Volume 102, Issue 6, Pages 737–745
DOI: https://doi.org/10.1134/S0001434617110128
Bibliographic databases:
Document Type: Article
UDC: 17.048
Language: Russian
Citation: A. I. Allilueva, A. I. Shafarevich, “Localized Asymptotic Solutions of the Linearized System of Magnetic Hydrodynamics”, Mat. Zametki, 102:6 (2017), 807–815; Math. Notes, 102:6 (2017), 737–745
Citation in format AMSBIB
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\paper Localized Asymptotic Solutions of the Linearized System of Magnetic Hydrodynamics
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\pages 737--745
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  • https://www.mathnet.ru/eng/mzm11735
  • https://doi.org/10.4213/mzm11735
  • https://www.mathnet.ru/eng/mzm/v102/i6/p807
    • This publication is cited in the following 2 articles:
    1. S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. I. Shafarevich, “Efficient asymptotics of solutions to the Cauchy problem with localized initial data for linear systems of differential and pseudodifferential equations”, Russian Math. Surveys, 76:5 (2021), 745–819  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. A. I. Allilueva, A. I. Shafarevich, “Localized solutions for linearized MHD equations and interaction of alfven modes”, Magnetohydrodynamics, 55:1-2, SI (2019), 15–21  crossref  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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