Bezrodnykh, S. I.; Vlasov, V. I. Asymptotics of the Riemann-Hilbert problem for a magnetic reconnection model in plasma. (English. Russian original) Zbl 1455.35259 Comput. Math. Math. Phys. 60, No. 11, 1839-1854 (2020); translation from Zh. Vychisl. Mat. Mat. Fiz. 60, No. 11, 1898-1914 (2020). Summary: 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 \(\varrho \to 0\) 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. Cited in 6 Documents MSC: 35Q85 PDEs in connection with astronomy and astrophysics 35Q15 Riemann-Hilbert problems in context of PDEs 76X05 Ionized gas flow in electromagnetic fields; plasmic flow 76W05 Magnetohydrodynamics and electrohydrodynamics 76L05 Shock waves and blast waves in fluid mechanics 35C20 Asymptotic expansions of solutions to PDEs 85A30 Hydrodynamic and hydromagnetic problems in astronomy and astrophysics Keywords:Riemann-Hilbert problem; conformal mapping; singular deformation of domain; asymptotics of solution; magnetic reconnection; Somov’s model; Syrovatskii’s current sheet PDFBibTeX XMLCite \textit{S. I. Bezrodnykh} and \textit{V. I. Vlasov}, Comput. Math. Math. Phys. 60, No. 11, 1839--1854 (2020; Zbl 1455.35259); translation from Zh. Vychisl. Mat. Mat. Fiz. 60, No. 11, 1898--1914 (2020) Full Text: DOI References: [1] Biskamp, D., Magnetic Reconnection in Plasmas (2000), Cambridge, UK: Cambridge Univ. 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