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Conservation laws for relativistic fluid dynamics. (English) Zbl 0909.76108

This paper presents a rigorous mathematical theory of relativistic fluid dynamics using equations developed by A. H. Taub [Annu. Rev. Fluid Mech. 10, 301–332 (1978; Zbl 0403.76097)]. Despite the complexity of the system, a complete analogy is established between classical and relativistic hydrodynamics. In particular, it is shown that the Newtonian limits of these results reduce to the classical results. To exclude the formation of a vacuum, the condition \(R_L> S_R\) is introduced, where \(R\) and \(S\) are Riemann invariants, \(R_L\) is the value of \(R\) at \(x\leq 0\), and \(S_R\) is the value of \(S\) at \(x>0\). The \((p,\nu)\)-plane is used in the analysis, and it is shown that it leads to the unique determination of the solution of the Riemann problem.

MSC:

76Y05 Quantum hydrodynamics and relativistic hydrodynamics
35L65 Hyperbolic conservation laws

Citations:

Zbl 0403.76097
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