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Global entropy solutions for isentropic relativistic fluid dynamics. (English) Zbl 0863.76099
The equations of conservation of baryon number and momentum for a one-dimensional relativistic fluid are considered in the Minkowski space-time with an equation of state \(p(\rho)= \sigma^2\rho\), where \(\sigma\) is a constant, \(\sigma^2<1\). A global entropy solution with a bounded variation with respect to the space variable is constructed. The technique of Nishida is applied to the Glimm difference scheme by an analysis of wave interactions in the plane of Riemann invariants. The Lorentz invariance properties of the system are involved to show that the shock curves based at different points are congruent in the plane of the Riemann invariants.

MSC:
76Y05 Quantum hydrodynamics and relativistic hydrodynamics
35Q75 PDEs in connection with relativity and gravitational theory
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
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