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 \(\varrho \to 0\) 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.
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Bezrodnykh, S.I., Vlasov, V.I. Asymptotics of the Riemann–Hilbert Problem for a Magnetic Reconnection Model in Plasma. Comput. Math. and Math. Phys. 60, 1839–1854 (2020). https://doi.org/10.1134/S0965542520110056
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DOI: https://doi.org/10.1134/S0965542520110056