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

TL;DR

This paper introduces an explicit set of eigenfunctions for the Stokes operator in 3D cylinders, demonstrating that these sets enable approximate controllability of Navier--Stokes equations under Lions boundary conditions.

Contribution

The paper constructs an explicit saturating set of eigenfunctions for the Stokes operator in 3D cylinders, establishing approximate controllability results.

Findings

Explicit saturating set of eigenfunctions proposed

Approximate controllability of Navier--Stokes in 3D cylinders proven

Saturating set facilitates control under Lions boundary conditions

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 $\rm 3D$ Cylinders under Lions boundary conditions.