Stabilizability of Two-Dimensional Navier-Stokes Equations with Help of a Boundary Feedback Control

被引:67
作者
Fursikov, A. V. [1 ]
机构
[1] Moscow MV Lomonosov State Univ, Dept Mech & Math, Moscow 119899, Russia
关键词
Oseen equations; Navier-Stokes equations; stabilization; extension operator; stable invariant manifold;
D O I
10.1007/PL00000972
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
For 2D Navier-Stokes equations defined in a bounded domain Omega we study stabilization of solution near a given steady-state flow (v) over cap (x) by means of feedback control defined on a part Gamma of boundary partial derivative Omega. New mathematical formalization of feedback notion is proposed. With its help for a prescribed number sigma > 0 and for an initial condition v(0)(x) placed in a small neighbourhood of (v) over cap (x) a control u(t, x'), x' is an element of Gamma, is constructed such that solution v(t, x) of obtained boundary value problem for 2D Navier-Stokes equations satisfies the inequality: parallel to v(t, .) - (v) over cap parallel to(H1) <= ce-(sigma t) for t >= 0. To prove this result we firstly obtain analogous result on stabilization for 2D Oseen equations.
引用
收藏
页码:259 / 301
页数:43
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