Gevrey regularity for Navier--Stokes equations under Lions boundary conditions

TL;DR

This paper proves Gevrey class regularity for the Navier--Stokes equations on various manifolds under Lions boundary conditions, extending known results to new geometries and dimensions.

Contribution

It establishes Gevrey regularity for Navier--Stokes equations on specific manifolds with Lions boundary conditions, including 2D and 3D cases, and revisits classical geometries.

Findings

Gevrey regularity proven in 2D rectangles, cylinders, and hemispheres.

Gevrey regularity established in 3D rectangles.

Revisits classical geometries like spheres and tori.

Abstract

The Navier--Stokes system is considered in a compact Riemannian manifold. Gevrey class regularity is proven under Lions boundary conditions: in 2D for the Rectangle, Cylinder, and Hemisphere, and in 3D for the Rectangle. The cases of the 2D Sphere and 2D and 3D Torus are also revisited.