scholarly journals TheH1-compact global attractor for the solutions to the Navier-Stokes equations in two-dimensional unbounded domains

Nonlinearity ◽  
2000 ◽  
Vol 13 (4) ◽  
pp. 1227-1238 ◽  
Author(s):  
Ning Ju
Keyword(s):  
Global Attractor ◽  
Stokes Equations ◽  
Unbounded Domains ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations

UPPER SEMICONTINUITY OF GLOBAL ATTRACTORS FOR 2D NAVIER–STOKES EQUATIONS

2012 ◽  
Vol 22 (03) ◽  
pp. 1250046 ◽  
Author(s):  
CAIDI ZHAO ◽  
JINQIAO DUAN
Keyword(s):  
Global Attractor ◽  
Stokes Equations ◽  
Upper Semicontinuity ◽  
Global Attractors ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Simply Connected

In this paper, the authors consider the two-dimensional Navier–Stokes equations defined on Ω = ℝ × (-L, L) and [Formula: see text], where [Formula: see text] is an expanding sequence of simply connected, bounded and smooth subdomains of Ω such that Ωm → Ω as m → ∞. Let [Formula: see text] and [Formula: see text] be the global attractors of the equations corresponding to Ω and Ωm, respectively, we establish that for any neighborhood [Formula: see text] of [Formula: see text], the global attractor [Formula: see text] enters [Formula: see text] if m is large enough.

The Estimation of the Hausdorff and Fractal Dimensions of the Global Attractor for 2D Autonomous g-Navier-Stokes Equations

2014 ◽  
Vol 511-512 ◽  
pp. 1235-1238
Author(s):  
Jin Ping Jiang ◽  
Xiao Xia Wang
Keyword(s):  
Sobolev Space ◽  
Global Attractor ◽  
Stokes Equations ◽  
Weighted Sobolev Space ◽  
Unbounded Domains ◽  
Fractal Dimensions ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Forcing Term ◽  
Hausdorff And Fractal Dimensions

In this paper, by using the energyequation method, the 2D g-Navier-Stokes equations with linear dampness on some unbounded domains wereinvestigated without the restriction of the forcing term belongingto some weighted Sobolev space. Moreover,the estimation of theHausdorff and Fractal dimensions of such attractors were alsoobtained.

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