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 The Exponential Attractors for the g-Navier-Stokes Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Delin Wu ◽  
Jicheng Tao
Keyword(s):  
Bounded Domain ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Exponential Attractor ◽  
Two Dimensional ◽  
Exponential Attractors ◽  
Navier Stokes Equations

We consider the exponential attractors for the two-dimensional g-Navier-Stokes equations in bounded domain Ω. We establish the existence of the exponential attractor inL2(Ω).

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.

scholarly journals On the Dimension of the Pullback Attractors for g-Navier-Stokes Equations

2010 ◽  
Vol 2010 ◽  
pp. 1-16 ◽  
Author(s):  
Delin Wu
Keyword(s):  
Fractal Dimension ◽  
Asymptotic Behaviour ◽  
Bounded Domain ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Pullback Attractor ◽  
Pullback Attractors ◽  
Navier Stokes Equations

We consider the asymptotic behaviour of nonautonomous 2D g-Navier-Stokes equations in bounded domainΩ. Assuming thatf∈Lloc2, which is translation bounded, the existence of the pullback attractor is proved inL2(Ω)andH1(Ω). It is proved that the fractal dimension of the pullback attractor is finite.

scholarly journals Attractors and Finite-Dimensional Behaviour in the 2D Navier-Stokes Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-29 ◽  
Author(s):  
James C. Robinson
Keyword(s):  
Dynamical Systems ◽  
Systems Approach ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Open Problems ◽  
Navier Stokes Equations ◽  
Infinite Dimensional ◽  
Infinite Dimensional Dynamical Systems ◽  
Finite Dimensional

The purpose of this review is to give a broad outline of the dynamical systems approach to the two-dimensional Navier-Stokes equations. This example has led to much of the theory of infinite-dimensional dynamical systems, which is now well developed. A second aim of this review is to highlight a selection of interesting open problems, both in the analysis of the two-dimensional Navier-Stokes equations and in the wider field of infinite-dimensional dynamical systems.

On the existence and uniqueness of solution to a stochastic 2D Allen–Cahn–Navier–Stokes model

2019 ◽  
Vol 19 (01) ◽  
pp. 1950007 ◽  
Author(s):  
Theodore Tachim Medjo
Keyword(s):  
Bounded Domain ◽  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Variational Solution ◽  
Uniqueness Of Solution ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Stochastic Version ◽  
Phase Parameter

We study, in this paper, a stochastic version of a coupled Allen–Cahn–Navier–Stokes model in a two-dimensional (2D) bounded domain. The model consists of the Navier–Stokes equations (NSEs) for the velocity, coupled with a Allen–Cahn model for the order (phase) parameter. We prove the existence and the uniqueness of a variational solution.

Direct simulation of transition in an oscillatory boundary layer

1998 ◽  
Vol 371 ◽  
pp. 207-232 ◽  
Author(s):  
G. VITTORI ◽  
R. VERZICCO
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Turbulent Regime ◽  
Two Dimensional ◽  
Temporal Development ◽  
Direct Simulation ◽  
Navier Stokes Equations ◽  
Oscillatory Boundary Layer

Numerical simulations of Navier–Stokes equations are performed to study the flow originated by an oscillating pressure gradient close to a wall characterized by small imperfections. The scenario of transition from the laminar to the turbulent regime is investigated and the results are interpreted in the light of existing analytical theories. The ‘disturbed-laminar’ and the ‘intermittently turbulent’ regimes detected experimentally are reproduced by the present simulations. Moreover it is found that imperfections of the wall are of fundamental importance in causing the growth of two-dimensional disturbances which in turn trigger turbulence in the Stokes boundary layer. Finally, in the intermittently turbulent regime, a description is given of the temporal development of turbulence characteristics.

Sign in / Sign up

Export Citation Format

Share Document