The incompressible Navier-Stokes equations on non-compact manifolds

Vittoria Pierfelice (1)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

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.

Mots clés: hyperbolic space; smoothing estimates; Bochner Laplacian; global well-posedness.; dispersive estimates; global well-posedness; Navier-Stokes equations; non-compact Riemannian manifolds; negative curvature

Domaines: Equations aux dérivées partielles [math.AP]

Vittoria Pierfelice. The incompressible Navier-Stokes equations on non-compact manifolds. Journal of Geometric Analysis, 2017, 27 (1), pp.577-617. ⟨hal-01002061⟩