Chen, Jing Conservation laws for relativistic fluid dynamics. (English) Zbl 0909.76108 Arch. Ration. Mech. Anal. 139, No. 4, 377-398 (1997). 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. Reviewer: A.Jeffrey (Newcastle upon Tyne) Cited in 23 Documents MSC: 76Y05 Quantum hydrodynamics and relativistic hydrodynamics 35L65 Hyperbolic conservation laws Keywords:analogy between classical and relativistic hydrodynamics; Newtonian limits; Riemann invariants; Riemann problem Citations:Zbl 0403.76097 PDFBibTeX XMLCite \textit{J. Chen}, Arch. Ration. Mech. Anal. 139, No. 4, 377--398 (1997; Zbl 0909.76108) Full Text: DOI