On well-posedness of relativistic theories for viscous fluids

Abstract:

Much effort has been invested during the last decades with the aim to develop a theory for dissipative fluids in the context of General Relativity. One of the difficulties that appear to that end is the parabolic nature of heat propagation, which seems to go against the causality principle imposed by Einstein's theory. This problem makes the issue of modelling relativistic viscous fluids a highly non-trivial task.

In this talk we shall review previous and current attempts at dissipative fluid theories. After recalling the necessary conditions for a general hydrodynamic theory to be well-posed, stable and causal, we shall point out some issues that appear when studying the corresponding initial-value formulation and finally comment on future challenges and open problems, both from the analytic and numerical perspectives.