Asymptotic solutions for MHD systems with a rapid jump near a moving surface. (15th December 2017) - Allilueva, Anna I; Shafarevich, Andrei I
Abstract: We study the Cauchy problem for a nonlinear system of Magnetohydrodynamics. The viscosity and conductivity are assumed to be small and the initial fields are assumed to jump rapidly near certain smooth 2D-surface in 3D-space. We construct formal asymptotic solution for this Cauchy problem. We study the spatial structure and time behavior of the solution. In particular, we derive free boundary problem for the limit values of the magnetic field and the velocity field of the fluid. This problem also governs the evolution of the surface of the jump. We derive equations on the moving surface, describing the evolution of the field profile. In particular, we prove that the effect of the instantaneous growth of the magnetic field takes place only for degenerate asymptotic modes.