Approximate controllability for Navier--Stokes equations in $3D$ rectangles under Lions boundary conditions

Abstract

The $3D$ Navier--Stokes system, under Lions boundary conditions, is proven to be approximately controllable provided a suitable saturating set does exist. An explicit saturating set for $3D$ rectangles is given.

21 pages

References in corpus (3)

• Euler equations are not exactly controllable by a finite-dimensional external force
• Gevrey regularity for Navier--Stokes equations under Lions boundary conditions
• Approximate controllability of Lagrangian trajectories of the 3D Navier-Stokes system by a finite-dimensional force

Cited by in corpus (1)

• Localized and degenerate controls for the incompressible Navier-Stokes system