Conservation laws for relativistic fluid dynamics
This paper presents a rigorous mathematical theory of relativistic fluid dynamics using equations developed by \textit{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.
analogy between classical and relativistic hydrodynamics
scientific article; zbMATH DE number 1096005