Borshch, Maxim S.; Zhdanov, Valery I.

Exact solutions of the equations of relativistic hydrodynamics representing potential flows

SIGMA, Symmetry Integrability Geom. Methods Appl. 3, Paper 116, 11 p., electronic only (2007)


Summary: We use a connection between relativistic hydrodynamics and scalar field theory to generate exact analytic solutions describing non-stationary inhomogeneous flows of the perfect fluid with one-parametric equation of state (EOS) $p = p(\epsilon )$. For linear EOS $p = \kappa \epsilon $ 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.

Mathematics Subject Classification

76Y05, 83C15, 83A05


relativistic hydrodynamics, exact solutions