Finite-dimensional Control for the Navier—Stokes Equations

2009 ◽  
pp. 105-111
Author(s):  
Alexander Yu. Chebotarev
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Dimensional Control ◽  
Navier Stokes Equations ◽  
Finite Dimensional

scholarly journals The Finite-Dimensional Uniform Attractors for the Nonautonomous g-Navier-Stokes Equations

2009 ◽  
Vol 2009 ◽  
pp. 1-17 ◽  
Author(s):  
Delin Wu
Keyword(s):  
Fractal Dimension ◽  
Bounded Domain ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Uniform Attractor ◽  
Navier Stokes Equations ◽  
Finite Dimensional ◽  
Uniform Attractors

We consider the uniform attractors for the two dimensional nonautonomous g-Navier-Stokes equations in bounded domain . Assuming , we establish the existence of the uniform attractor in and . The fractal dimension is estimated for the kernel sections of the uniform attractors obtained.

scholarly journals Stabilization of the non-homogeneous Navier–Stokes equations in a 2d channel

2019 ◽  
Vol 25 ◽  
pp. 66
Author(s):  
Sourav Mitra
Keyword(s):  
Feedback Control ◽  
Poiseuille Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Boundary Stabilization ◽  
Navier Stokes Equations ◽  
Local Boundary ◽  
Hyperbolic Dynamics ◽  
Finite Dimensional ◽  
Dimensional Range

In this article, we study the local boundary stabilization of the non-homogeneous Navier–Stokes equations in a 2d channel around Poiseuille flow which is a stationary solution for the system under consideration. The feedback control operator we construct has finite dimensional range. The homogeneous Navier–Stokes equations are of parabolic nature and the stabilization result for such system is well studied in the literature. In the present article we prove a stabilization result for non-homogeneous Navier–Stokes equations which involves coupled parabolic and hyperbolic dynamics by using only one boundary control for the parabolic part.

scholarly journals Stochastic Navier-Stokes Equations with Artificial Compressibility in Random Durations

2010 ◽  
Vol 2010 ◽  
pp. 1-24 ◽  
Author(s):  
Hong Yin
Keyword(s):  
Incompressible Flow ◽  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Bounded Domains ◽  
Two Dimensional ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Artificial Compressibility ◽  
Finite Dimensional

The existence and uniqueness of adapted solutions to the backward stochastic Navier-Stokes equation with artificial compressibility in two-dimensional bounded domains are shown by Minty-Browder monotonicity argument, finite-dimensional projections, and truncations. Continuity of the solutions with respect to terminal conditions is given, and the convergence of the system to an incompressible flow is also established.

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