Gevrey regularity for Navier–Stokes equations under Lions boundary conditions

Abstract

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. MSC2010: 35Q30, 76D03.

Approximate controllability for Navier–Stokes equations in \rm3D cylinders under Lions boundary conditions by an explicit saturating set

“…Lions boundary condition is a particular case of Navier boundary conditions. For works and motivations concerning Lions and Navier boundary conditions (in both 2D and 3D cases) we refer to [6,10,11,16,17,30,31] and references therein.…”

Approximate Controllability for Navier–Stokes Equations in 3D Rectangles Under Lions Boundary Conditions

“…Base step By definition we have that C = C 4 C ⊃ C 4 ZC and span C = G 0 . Therefore Inclusion (16) holds for q = 4.…”

“…and that the orthogonality of the family {w j(k),k | j(k) ∈ {1, 2 − # 0 (k)}} implies that the family in (14a) is also orthogonal. The completeness of the system in (14a) is shown in [21,Section 6.6].…”

“…Lions boundary conditions are a particular case of Navier boundary conditions. For works and motivations concerning Lions and Navier boundary conditions (in both 2D and 3D cases) we refer to [6,10,11,16,30,31] and references therein.…”