Abstract
Abstract 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.
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