Exact Solutions of the Equations of Relativistic Hydrodynamics Representing Potential Flows

Abstract

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.

This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007, Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

References in corpus (4)

• Dynamics of dark energy
• A New Family of Simple Solutions of Perfect Fluid Hydrodynamics
• Detailed description of accelerating, simple solutions of relativistic perfect fluid hydrodynamics
• A Co-moving Coordinate System for Relativistic Hydrodynamics

Cited by in corpus (1)

• Exact (1+1)-dimensional flows of a perfect fluid