Navier-Stokes Equation on the Rectangle
Optimization and Control
2007-05-23 v1
Abstract
We study controllability issues for the Navier-Stokes Equation on a two dimensional rectangle with so-called Lions boundary conditions. Rewriting the Equation using a basis of harmonic functions we arrive to an infinite-dimensional system of ODEs. Methods of Geometric/Lie Algebraic Control Theory are used to prove controllability by means of low modes forcing of finite-dimensional Galerkin approximations of that system. Proving the continuity of the ``control solution'' map in the so-called relaxation metric we use it to prove both solid controllability on observed component and -approximate controllability of the Equation (full system) by low modes forcing.
Cite
@article{arxiv.math/0504323,
title = {Navier-Stokes Equation on the Rectangle},
author = {Sérgio Rodrigues},
journal= {arXiv preprint arXiv:math/0504323},
year = {2007}
}