Abstract
AbstractThis chapter is devoted to the conditions under which nonlinear hydrodynamical waves are produced and to the study of the flow properties across such waves. Special emphasis is given to the mathematics of hyperbolic systems of partial differential equations, showing that the relativistic-hydrodynamics equations can be cast in both quasi-linear hyperbolic form and in conservative form. Attention is focused to the discussion of rarefaction and shock waves, which are treated to highlight the similarities and also the differences with Newtonian physics. Within this framework, the Riemann problem for the relativistic-hydrodynamics equations in flat spacetime is studied in great detail, both for one-dimensional and multidimensional flows. The chapter is completed by two more advanced topics, namely the stability of nonlinear waves and the properties of discontinuous solutions in full general relativity.
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