Abstract
We study asymptotic solutions of the nonlinear system of MagnetoHydrodynamics. The solutions are assumed to jump rapidly near certain 2D-surface in 3D-space. We study the 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 governs also 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. This effect is deeply connected with non-Hermitian structure of the linearized induction operator.
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Acknowledgments
The work was partially supported by the Russian Foundation of Fundamental Research (grants 16-31-00339, 16-01-00378, 14-01-00521a) and the grant of the support of leading scientific schools (581.2014.1).
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Allilueva, A.I., Shafarevich, A.I. (2016). Geometrical and Asymptotical Properties of Non-Selfadjoint Induction Equation with the Jump of the Velocity Field. Time Evolution and Spatial Structure of the Magnetic Field. In: Bagarello, F., Passante, R., Trapani, C. (eds) Non-Hermitian Hamiltonians in Quantum Physics. Springer Proceedings in Physics, vol 184. Springer, Cham. https://doi.org/10.1007/978-3-319-31356-6_2
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DOI: https://doi.org/10.1007/978-3-319-31356-6_2
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