Exact Solutions of the Equations of Relativistic Hydrodynamics Representing Potential Flows

Exact Solutions of the Equations of Relativistic Hydrodynamics Representing Potential Flows

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(ε). For linear EOS p = κε we obtain self-similar solutions in the case of plane, cylindrical and spherical symmetries. In the case of extremely stiff EOS (κ = 1) we...

Exact solutions of the equations of relativistic hydrodynamics

We use a connection between relativistic hydrodynamics and scalar field theory to generate analytic solutions describing non-stationary non-homogeneous flows of the relativistic perfect fluid with barotropic equation of state (EOS). For linear EOS p = κε we obtain selfsimilar solutions in case of plane, cylindrical and spherical symmetries. Besides, in case of extremely stiff EOS (p = ε) we obt...

New exact solutions of relativistic hydrodynamics

A new class of simple and exact solutions of relativistic hydrodynamics is presented, and the consequences are explored in data analysis. The effects of longitudinal work and acceleration are taken into account in an advanced estimate of the initial energy density and the life-time of the reaction.

Exact solutions of nonlinear interval Volterra integral equations

Analytic solutions of hydrodynamics equations

Many similarity solutions have been found for the equations of one-dimensional (1-D) hydrodynamics. These special combinations of variables allow the partial differential equations to be reduced to ordinary differential equations, which must then be solved to determine the physical solutions. Usually, these reduced ordinary differential equations are solved numerically. In some cases it is poss...