Asymptotics of the Riemann–Hilbert Problem for the Somov Model of Magnetic Reconnection of Long Shock Waves

• Published in: Mathematical Notes Vol. 110; no. 5-6; pp. 853 - 871
• Main Authors: Bezrodnykh, S. I., Vlasov, V. I.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01-11-2021
• Subjects: 14/34; 639/766/189; 639/766/530; 639/766/747; Mathematics; Mathematics and Statistics; asymptotics of a solution; Somov model; Petschek model; conformal mapping; singular deformation of a domain; effect of magnetic reconnection; Riemann–Hilbert problem
• ISSN: 0001-4346; 1573-8876
• DOI: 10.1134/S0001434621110225

We consider the Riemann–Hilbert problem in a domain of complicated shape (the exterior of a system of cuts), with the condition of growth of the solution at infinity. Such a problem arises in the Somov model of the effect of magnetic reconnection in the physics of plasma, and its solution has the physical meaning of a magnetic field. The asymptotics of the solution is obtained for the case of infinite extension of four cuts from the given system, which have the meaning of shock waves, so that the original domain splits into four disconnected components in the limit. It is shown that if the coefficient in the condition of growth of the magnetic field at infinity consistently decreases in this case, then this field basically coincides in the limit with the field arising in the Petschek model of the effect of magnetic reconnection.