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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2008, Volume 49, Issue 5, Pages 27–40
(Mi pmtf1947)
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This article is cited in 2 scientific papers (total in 2 papers)
Ovsyannikov plane vortex: The equations of the submodel
S. V. Golovin Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Abstract:
A submodel of the equations of ideal magnetohydrodynamics is constructed that generalizes the classical motion of an ideal continuous medium with plane waves. It is shown that, in contrast to classical motion, in this submodel the velocity and magnetic-field vectors can change direction in a plane orthogonal to a distinguished spatial direction. The submodel is described by a system of equations with two independent variables and a finite relation specifying the orientation of the vector fields in space. The solutions of the submodel define substantially spatial processes and singularities in the motion of continuous media which cannot be studied in the classical one-dimensional formulation.
Keywords:
ideal magnetohydrodynamics, partially invariant solutions, overdetermined systems of differential equations, singularities in the motion of a continuous medium.
Received: 30.07.2007 Accepted: 05.09.2007
Citation:
S. V. Golovin, “Ovsyannikov plane vortex: The equations of the submodel”, Prikl. Mekh. Tekh. Fiz., 49:5 (2008), 27–40; J. Appl. Mech. Tech. Phys., 49:5 (2008), 725–736
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https://www.mathnet.ru/eng/pmtf1947 https://www.mathnet.ru/eng/pmtf/v49/i5/p27
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