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.

25 pages

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Cited by in corpus (6)

• Causality and existence of solutions of relativistic viscous fluid dynamics with gravity
• The formulation of the Navier-Stokes equations on Riemannian manifolds
• Recent developments in mathematical aspects of relativistic fluids
• Bianchi I cosmology in the presence of a causally regularized viscous fluid
• New symmetry in higher curvature spacetimes
• Symmetry evolution for the imperfect fluid under perturbations