Random attractor for the stochastic Cahn–Hilliard–Navier–Stokes system with small additive noise

2018 ◽  
Vol 36 (3) ◽  
pp. 546-559 ◽  
Author(s):  
Fang Li ◽  
Bo You
Keyword(s):  
Stokes System ◽  
Additive Noise ◽  
Random Attractor ◽  
Navier Stokes ◽  
Small Additive

scholarly journals Random Attractors for Stochastic Retarded 2D-Navier-Stokes Equations with Additive Noise

2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
Xiaoyao Jia ◽  
Xiaoquan Ding
Keyword(s):  
Additive Noise ◽  
Stochastic Equation ◽  
Stokes Equations ◽  
Upper Semicontinuity ◽  
Random Attractor ◽  
Navier Stokes ◽  
Pullback Attractor ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Random Attractors

In this paper, the existence and the upper semicontinuity of a pullback attractor for stochastic retarded 2D-Navier-Stokes equation on a bounded domain are obtained. We first transform the stochastic equation into a random equation and then obtain the existence of a random attractor for random equation. Then conjugation relation between two random dynamical systems implies the existence of a random attractor for the stochastic equation. At last, we get the upper semicontinuity of random attractor.

scholarly journals Some preliminary observations on a defect Navier–Stokes system

2019 ◽  
Vol 347 (10) ◽  
pp. 677-684 ◽  
Author(s):  
Amit Acharya ◽  
Roger Fosdick
Keyword(s):  
Stokes System ◽  
Navier Stokes

scholarly journals Asymptotic analysis of an optimal control problem for a viscous incompressible fluid with Navier slip boundary conditions

2021 ◽  
pp. 1-21
Author(s):  
Claudia Gariboldi ◽  
Takéo Takahashi
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Boundary Conditions ◽  
Control Problem ◽  
Stokes System ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Navier Slip ◽  
Slip Boundary ◽  
Navier Slip Boundary Conditions

We consider an optimal control problem for the Navier–Stokes system with Navier slip boundary conditions. We denote by α the friction coefficient and we analyze the asymptotic behavior of such a problem as α → ∞. More precisely, we prove that if we take an optimal control for each α, then there exists a sequence of optimal controls converging to an optimal control of the same optimal control problem for the Navier–Stokes system with the Dirichlet boundary condition. We also show the convergence of the corresponding direct and adjoint states.

Sign in / Sign up

Export Citation Format

Share Document