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, Syrovatskii’s current sheet.
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