Approximate controllability for Navier--Stokes equations in {\rm 3D} Cylinders under Lions boundary conditions by an explicit saturating set

Abstract

An explicit saturating set consisting of eigenfunctions of Stokes operator in general 3D Cylinders is proposed. The existence of saturating sets implies the approximate controllability for Navier--Stokes equations in $3D$ Cylinders under Lions boundary conditions.

arXiv comment33 pages, 4 figures. arXiv admin note: text overlap with arXiv:1712.04900

References in corpus (6)

• Controllability of 2D Euler and Navier-Stokes Equations by Forcing 4 Modes
• Sharp estimates for the number of degrees of freedom for the damped-driven 2D Navier--Stokes equations
• Exact controllability in projections for three-dimensional Navier-Stokes equations
• On finite-dimensional projections of distributions for solutions of randomly forced PDE's
• Euler equations are not exactly controllable by a finite-dimensional external force
• Gevrey regularity for Navier--Stokes equations under Lions boundary conditions