New Solutions of Viscous Relativistic Hydrodynamics

New, spherical solutions of non-relativistic, dissipative hydrodynamics

“…This behaviour is also perceived in ref. [16], that as far as we know presents the first exact solutions of the relativistic Navier-Stokes equations for non-zero bulk viscosities.…”

“…This motivated us to investigate the non-relativistic and spherically symmetric limit of the relativistic exact solutions described in refs. [16,17]. It turned out that in this limit we obtained new, simple and exact solutions of the non-relativistic Navier-Stokes equations.…”

“…[15]. Dissipation in relativistic hydrodynamics have been addressed in an exact form as well by two recent manuscripts [16,17]. These works discuss analytic results on the effect of bulk viscosity on 1+3 dimensional exact solutions of the relativistic Navier-Stokes as well as the Israel-Stewart equations, generalizing the Hwa-Bjorken solution for non vanishing kinematic bulk viscosities in 1+3 dimensions [16,17].…”

“…Dissipation in relativistic hydrodynamics have been addressed in an exact form as well by two recent manuscripts [16,17]. These works discuss analytic results on the effect of bulk viscosity on 1+3 dimensional exact solutions of the relativistic Navier-Stokes as well as the Israel-Stewart equations, generalizing the Hwa-Bjorken solution for non vanishing kinematic bulk viscosities in 1+3 dimensions [16,17]. The velocity field of these solutions is also a Hubble-flow, which describes reasonably well the asymptotic velocity profile of small and exploding fireballs, with possible applications even in high energy heavy ion collisions [17].…”

“…It seems to us that the new solutions of refs. [16,17] provide a great tool to investigate the late time effects of bulk viscosity in the hydrodynamic evolution. However, the fundamental equations of dissipative, relativistic hydrodynamics are debatable and so far several schemes have been proposed, but without a fundamental and generally accepted method, that are able to provide a stable and causal theory, and at the same time have also the correct nonrelativistic limit: the non-relativistic Navier-Stokes equations.…”