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

Abstract

<p style='text-indent:20px;'>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 <inline-formula><tex-math id="M2">\begin{document}$ \rm 3D $\end{document}</tex-math></inline-formula> Cylinders under Lions boundary conditions.