5 papers · 1 filter
Global exponential stability for the three-dimensional Navier-Stokes equations on hyperbolic space
Zhi-Wei Wang, Samuel L. Braunstein
We prove that the three-dimensional incompressible Navier-Stokes equations with the deformation Laplacian on hyperbolic 3-space $\HH^3$ admit a unique global mild solution for suff…
Resolving the viscosity operator ambiguity on Riemannian manifolds via a kinematic selection principle
Zhi-Wei Wang, Samuel L. Braunstein
On a general Riemannian manifold the Navier-Stokes equations admit several inequivalent formulations, differing in the choice of viscous operator: the Hodge Laplacian, the Bochner…
Logarithmic Sobolev inequality and hypercontractivity for the Navier-Stokes Fokker-Planck operator
Zhi-Wei Wang, Samuel L. Braunstein
The stochastic incompressible Navier-Stokes equations on $\TT^3$, completed by the fluctuation-dissipation noise, have a Fokker-Planck generator that decomposes into a self-adjoint…
Exponential thermalisation of viscous fluids on negatively curved manifolds
Samuel L. Braunstein, Zhi-Wei Wang
The deterministic incompressible Navier-Stokes equations are physically incomplete: any viscous fluid at finite temperature must exhibit thermal fluctuations whose form is dictated…
Boundary conditions select the viscous operator on Riemannian hypersurfaces: formal analysis and rigorous thin-shell limits
Zhi-Wei Wang, Samuel L. Braunstein
A viscous fluid confined to a thin layer around a curved surface is governed, as the layer thickness vanishes, by an effective viscous operator on the surface. We show that the wal…