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Abstract: This paper uses products of distributions to obtain new junction conditionsfor relativistic shocks. In general, the shock is accompanied by a surfacelayer, and the new conditions generalize both Taub-s jump conditions forshocks, and those of Israel and Kuchar for surface layers. In thenon-relativistic limit, the surface layer is present only when the fluid isviscous or thermally conducting-a situation where the classicalRankine-Hugoniot conditions do not apply. Thus, our conditions properly extendall previous conditions, and provide complete Cauchy data needed to solve thefull Navier-Stokes equations downstream of the shock. Since the associative lawfails for our product, the residual uncertainty regarding the association offactors must be eliminated empirically. This is equivalent to fixing thecorrect initial form of the equations such as the ``conservation form- inthe Euler case



Author: C. K. Raju

Source: https://arxiv.org/







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