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Stability of strong discontinuities in fluids and MHD. (English) Zbl 1231.76344
Friedlander, S. (ed.) et al., Handbook of mathematical fluid dynamics. Vol. 1. Amsterdam: Elsevier (ISBN 0-444-50330-7). 545-652 (2002).
Summary: This chapter is devoted to the issue of stability of strong discontinuities in fluids and magnetohydrodynamics (MHD) and surveys main known results in this field. All the main points in the stability analysis are demonstrated on the example of shock waves in ideal models of gas dynamics, relativistic gas dynamics, and MHD. Ideal MHD is a good example containing, besides shock waves, different other types of strong discontinuities. Other MHD discontinuities include contact, tangential, and rotational discontinuities. The issue of stability for all these MHD discontinuities is also examined in this chapter. The main attention is concentrated on the linearized stability analysis and the issue of uniform stability. The issue of structural (nonlinear) stability is briefly discussed for gas dynamical shock waves. Open problems and future directions are discussed in the end of the chapter.
For the entire collection see [Zbl 0992.76001].

MSC:
76W05 Magnetohydrodynamics and electrohydrodynamics
76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
76E99 Hydrodynamic stability
35L67 Shocks and singularities for hyperbolic equations
35B35 Stability in context of PDEs
35Q35 PDEs in connection with fluid mechanics
76L05 Shock waves and blast waves in fluid mechanics
76N15 Gas dynamics (general theory)
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