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Global exponential stability for the three-dimensional Navier-Stokes equations on hyperbolic space
Announce Type: replace-cross Abstract: 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 sufficiently small initial data in $L^3(\HH^3)$, and that this solution decays exponentially to zero. The exponential decay rate is $\mu\lambda_\Def^{(3)}$, where $\mu$ is the dynamic viscosity and $\lambda_\Def^{(3)} = 26/9$ is the effective spectral gap of the deformation...