Liouville theorems for the Stationary Navier Stokes equation on a hyperbolic space

TL;DR

This paper investigates Liouville theorems for the stationary Navier-Stokes equations on hyperbolic spaces, extending known results to non-Euclidean geometries and more general manifolds.

Contribution

It provides new Liouville theorems for stationary Navier-Stokes equations on hyperbolic spaces and other manifolds, filling a gap in understanding these equations in non-Euclidean settings.

Findings

Liouville theorems established for hyperbolic spaces

Extension of results to other dimensions and manifolds

Addresses open problem for 3D hyperbolic Navier-Stokes equations

Abstract

The problem for the stationary Navier-Stokes equation in 3D under finite Dirichlet norm is open. In this paper we answer the analogous question on the 3D hyperbolic space. We also address other dimensions and more general manifolds.