Boundary Stabilization of the Navier-Stokes Equations in the Case of Mixed Boundary Conditions
Boundary Stabilization of the Navier-Stokes Equations in the Case of Mixed Boundary Conditions
复制标题
混合边界条件下纳维-斯托克斯方程的边界稳定
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
J. Raymond
中科院分区：
文献类型：
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作者：
P. Nguyen;J. Raymond
我们研究了由具有混合边界条件的纳维-斯托克斯方程描述的二维流体流动围绕不稳定稳态解的边界反馈稳定性。该控制是局部狄利克雷边界控制。通过稳定不稳定稳态解周围的线性纳维-斯托克斯方程来确定反馈控制律。我们证明了线性反馈定律局部稳定了纳维-斯托克斯系统。因此，我们将先前已知的几何域边界规则且仅存在狄利克雷边界条件的情况下的结果扩展到具有混合边界条件的情况。
We study the boundary feedback stabilization, around an unstable stationary solution, of a two dimensional fluid flow described by the Navier--Stokes equations with mixed boundary conditions. The control is a localized Dirichlet boundary control. A feedback control law is determined by stabilizing the linearized Navier--Stokes equations around the unstable stationary solution. We prove that the linear feedback law locally stabilizes the Navier--Stokes system. Thus, we extend results previously known in the case when the boundary of the geometrical domain is regular and when only Dirichlet boundary conditions are present to the case with mixed boundary conditions.
影响因子：
3
作者：
P. Benner;J. Saak;F. Schieweck;P. Skrzypacz;H. Weichelt
通讯作者：
P. Benner;J. Saak;F. Schieweck;P. Skrzypacz;H. Weichelt