On the well-posedness of relativistic viscous fluids with non-zero vorticity

Abstract: We study the problem of coupling Einstein's equations to a relativistic and physically well-motivated version of the Navier-Stokes equations. Under a natural evolution condition for the vorticity, we prove existence and uniqueness in a suitable Gevrey class if the fluid is incompressible, where this condition is given an appropriate relativistic interpretation, and show that the solutions enjoy the finite propagation speed property.