Gevrey regularity for Navier--Stokes equations under Lions boundary   conditions
  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. 
Duy Phan and S\'ergio S. Rodrigues
math.AP