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 a 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.