Navier-Stokes Equation on the Rectangle
| dc.creator | Rodrigues, Sérgio | |
| dc.date | 2005-04-15 | |
| dc.date.accessioned | 2026-07-07T06:33:08Z | |
| dc.date.available | 2026-07-07T06:33:08Z | |
| dc.description | 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 $\mapsto$ solution'' map in the so-called relaxation metric we use it to prove both solid controllability on observed component and $\mathbf L^2$-approximate controllability of the Equation (full system) by low modes forcing. | |
| dc.identifier | https://arxiv.org/abs/math/0504323 | |
| dc.identifier | http://arxiv.org/abs/math/0504323 | |
| dc.identifier | J. Dyn. Cont. Systems, vol 12, no 4, 2006 (517-562) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99098 | |
| dc.subject | Optimization and Control | |
| dc.title | Navier-Stokes Equation on the Rectangle | |
| dc.type | text |