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Zh. Vychisl. Mat. Mat. Fiz., 2020, Volume 60, Number 11, Pages 1898–1914 (Mi zvmmf11160)  

This article is cited in 1 scientific paper (total in 1 paper)

Partial Differential Equations

Asymptotics of the Riemann–Hilbert problem for a magnetic reconnection model in plasma

S. I. Bezrodnykhab, V. I. Vlasovac

a Federal Research Center "Computer Science and Control", Russian Academy of Sciences, Moscow, 119333 Russia
b Sternberg Astronomical Institute, Moscow State University, Moscow, 119992 Russia
c Moscow Center of Fundamental and Applied Mathematics, Lomonosov Moscow State University, Moscow, 119991 Russia

Abstract: For the Riemann–Hilbert problem in a singularly deformed domain, an asymptotic expansion is found that corresponds to the limit transition from Somov's magnetic reconnection model to Syrovatskii's one as the relative shock front length $\varrho$ tends to zero. It is shown that this passage to the limit corresponding to $\varrho\to0$ is performed with the preservation of the reverse current region, while the parameter determining magnetic field refraction on shock waves grows as $\varrho^{-1/2}$. Moreover, the correction term to the Syrovatskii field has the order of $\rho$ and decreases in an inverse proportion to the distance from the current configuration.

Key words: Riemann–Hilbert problem, conformal mapping, singular deformation of domain, asymptotics of solution, magnetic reconnection, Somov's model, SyrovatskiiТs current sheet.

DOI: https://doi.org/10.31857/S0044466920110058


English version:
Computational Mathematics and Mathematical Physics, 2020, 60:11, 1839–1854

Bibliographic databases:

UDC: 519.642
Received: 13.05.2020
Revised: 03.06.2020
Accepted:07.07.2020

Citation: S. I. Bezrodnykh, V. I. Vlasov, “Asymptotics of the Riemann–Hilbert problem for a magnetic reconnection model in plasma”, Zh. Vychisl. Mat. Mat. Fiz., 60:11 (2020), 1898–1914; Comput. Math. Math. Phys., 60:11 (2020), 1839–1854

Citation in format AMSBIB
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\paper Asymptotics of the Riemann--Hilbert problem for a magnetic reconnection model in plasma
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2020
\vol 60
\issue 11
\pages 1898--1914
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\crossref{https://doi.org/10.31857/S0044466920110058}
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\transl
\jour Comput. Math. Math. Phys.
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\issue 11
\pages 1839--1854
\crossref{https://doi.org/10.1134/S0965542520110056}
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    This publication is cited in the following articles:
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  • ∆урнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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