Exact controllability of the Galerkin approximations of Navier-Stokes equations

被引：4

作者：

Lions, JL ^{[1
]}

Zuazua, E ^{[1
]}

机构：

[1] UNIV COMPLUTENSE MADRID,DEPT MATEMAT APLICADA,E-28040 MADRID,SPAIN

来源：

COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE | 1997年 / 324卷 / 09期

关键词：

D O I：

10.1016/S0764-4442(97)87878-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider Navier-Stokes equations in a smooth domain of R-n, n = 2, 3, with Dirichlet boundary conditions. We introduce the classical Galerkin approximation and study its exact controllability when the control acts on an open non-empty subset of the domain. Under suitable assumptions on the elements of the Galerkin basis, we prove that this finite-dimensional system is exactly controllable. The proof combines HUM together with a classical fixed point argument, and relies on the cancellation properties of the non-linearity appearing in the Navier-Stokes equations.

引用

页码：1015 / 1021

页数：7