Stability of Strong Discontinuities in Magnetohydrodynamics and Electrohydrodynamics

Download or read book Stability of Strong Discontinuities in Magnetohydrodynamics and Electrohydrodynamics written by Aleksandr Mikhaĭlovich Blokhin and published by Nova Publishers. This book was released on 2003 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph examines multidimensional stability of strong discontinuities (e.g. shock waves) for systems of conservation laws and surveys the author's results for models of ideal magnetohydrodynamics (classical, 'pressure anisotropic', relativistic) and electrohydrodynamics. The primary attention is concentrated on linearised stability analysis, especially on the issue of uniform stability in the sense of the uniform Kreiss-Lopatinski condition. A so-called 'equational' approach based on obtaining, by the dissipative integrals technique, a priori estimates without loss of smoothness for corresponding linearised stability problems in the domains of uniform stability is described. Recent results for ideal models of MHD (classical MHD, 'pressure anisotropic' MHD of Chew, Goldberger and Low, relativistic MHD) and also for a certain non-hyperbolic model are presented as the system of electrohydrodynamics (EHD).