Unique global mild solutions to 3D NS on H^3 with small L^3 data decay exponentially at rate μ times 26/9 due to curvature-induced spectral gap of the deformation Laplacian.
Donnelly, The differential form spectrum of hyperbolic space, Manuscripta Math.33 (1981) 365–385
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Global exponential stability for the three-dimensional Navier-Stokes equations on hyperbolic space
Unique global mild solutions to 3D NS on H^3 with small L^3 data decay exponentially at rate μ times 26/9 due to curvature-induced spectral gap of the deformation Laplacian.