The incompressible Navier-Stokes equations on non-compact manifolds

Vittoria Pierfelice

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arXiv · 1406.1644

The incompressible Navier-Stokes equations on non-compact manifolds

Vittoria Pierfelice

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Abstract

We shall prove dispersive and smoothing estimates for Bochner type laplacians on some non-compact Riemannian manifolds with negative Ricci curvature, in particular on hyperbolic spaces. These estimates will be used to prove Fujita-Kato type theorems for the incompressible Navier-Stokes equations. We shall also discuss the uniqueness of Leray weak solutions in the two dimensional case.

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Vittoria Pierfelice. 2014-06-06. The incompressible Navier-Stokes equations on non-compact manifolds. https://arxiv.org/abs/1406.1644

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