On the well-posedness of relativistic viscous fluids

Using a simple and well-motivated modification of the stress-energy tensor for a viscous fluid proposed by Lichnerowicz, we prove that Einstein's equations coupled to a relativistic version of the Navier-Stokes equations are well-posed in a suitable Gevrey class if the fluid is incompressible and irrotational. These last two conditions are given an appropriate relativistic interpretation. The solutions enjoy the domain of dependence or finite propagation speed property. We also derive a full set of equations, describing a relativistic fluid that is not necessarily incompressible or irrotational, which is well-suited for comparisons with the system of an inviscid fluid.