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Exact solutions of the equations of relativistic hydrodynamics representing potential flows. (English) Zbl 1131.76062
Summary: We use a connection between relativistic hydrodynamics and scalar field theory to generate exact analytic solutions describing non-stationary inhomogeneous flows of perfect fluid with one-parametric equation of state (EOS) \(p=p(\varepsilon)\). For linear EOS \(p=\kappa\varepsilon\) we obtain self-similar solutions in the case of plane, cylindrical and spherical symmetries. In the case of extremely stiff EOS \((\kappa=1)\) we obtain “monopole + dipole” and “monopole + quadrupole” axially symmetric solutions. We also found some nonlinear EOSs that admit analytic solutions.

76Y05 Quantum hydrodynamics and relativistic hydrodynamics
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
76M55 Dimensional analysis and similarity applied to problems in fluid mechanics
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