Observer-Based Feedback Boundary Stabilization of the Navier-Stokes Equations
This paper aims at designing an observer-based feedback law which locally stabilizes the solution to the two dimensional Navier—Stokes equations with mixed boundary conditions. We consider a finite number of controls acting on a portion of the boundary through Robin boundary conditions and construct a linear Luenberger observer based on the point observations of the linearized Navier-Stokes equations. The sensor location for the point observations is determined by the response of feedback functional gains. We prove that the nonlinear system coupled with the observer through the feedback law is locally exponentially stable. Numerical experiments based on a Taylor—Hood finite element method are presented to illustrate the design for different Reynolds numbers.
X. He et al., "Observer-Based Feedback Boundary Stabilization of the Navier-Stokes Equations," Computer Methods in Applied Mechanics and Engineering, vol. 339, pp. 542-566, Elsevier B.V., Sep 2018.
The definitive version is available at https://doi.org/10.1016/j.cma.2018.05.008
Mathematics and Statistics
Keywords and Phrases
Feedback stabilization; Luenberger observer; Mixed boundary conditions; Navier-Stokes equations; Point observation
International Standard Serial Number (ISSN)
Article - Journal
© 2018 Elsevier B.V., All rights reserved.
01 Sep 2018