Relativistic dissipative fluids

In general relativity we don't have any preferred time function, so we can not have infinite propagation speeds. Thus, parabolic systems like the Navier-Stokes equations are not possible. To overcome this several proposals for admissible theories have been put forward in the past.

Notably, the first ones were ill posed, namely a small variation on the initial data produced huge differences on the solutions. Fortunately new proposals have arised which are well posed. Here we discuss one of them. In particular we shall concentrate on one describing conformally invariant fluids, the limit when the particle's mass is much smaller than their thermal speeds.

In this case the universe of possible theories collapses to a four parameter family, Only one of them related to the propagation speeds of the system. This case is well posed. We shall further discuss some simulations exploring these free parameter variations and some efforts to construct algorithms to automatically generate computer codes for solving them.