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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.

MSC:
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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