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 Generalized Navier–Stokes Equations and Dynamics of Plane Molecular Media

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 288
Author(s):  
Alexei Kushner ◽  
Valentin Lychagin
Keyword(s):  
Carbon Dioxide ◽  
Internal Structure ◽  
Stokes Equation ◽  
Hydrogen Cyanide ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations

The first analysis of media with internal structure were done by the Cosserat brothers. Birkhoff noted that the classical Navier–Stokes equation does not fully describe the motion of water. In this article, we propose an approach to the dynamics of media formed by chiral, planar and rigid molecules and propose some kind of Navier–Stokes equations for their description. Examples of such media are water, ozone, carbon dioxide and hydrogen cyanide.

A note on the solution of the Navier-Stokes equations for a spherically symmetric expansion into a very low pressure

1973 ◽  
Vol 59 (2) ◽  
pp. 391-396 ◽  
Author(s):  
N. C. Freeman ◽  
S. Kumar
Keyword(s):  
Shock Wave ◽  
Reynolds Number ◽  
Stokes Equation ◽  
Stokes Equations ◽  
Low Pressure ◽  
Navier Stokes ◽  
Spherically Symmetric ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Type Flow

It is shown that, for a spherically symmetric expansion of a gas into a low pressure, the shock wave with area change region discussed earlier (Freeman & Kumar 1972) can be further divided into two parts. For the Navier–Stokes equation, these are a region in which the asymptotic zero-pressure behaviour predicted by Ladyzhenskii is achieved followed further downstream by a transition to subsonic-type flow. The distance of this final region downstream is of order (pressure)−2/3 × (Reynolds number)−1/3.

The Onset of Turbulence: Insights Into the Navier-Stokes Equations

2017 ◽  
Author(s):  
Carl E. Rathmann
Keyword(s):  
Stokes Equations ◽  
Direct Consequence ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Fluid Behavior ◽  
Onset Of Turbulence ◽  
And Mathematics ◽  
High Reynolds

For well over 150 years now, theoreticians and practitioners have been developing and teaching students easily visualized models of fluid behavior that distinguish between the laminar and turbulent fluid regimes. Because of an emphasis on applications, perhaps insufficient attention has been paid to actually understanding the mechanisms by which fluids transition between these regimes. Summarized in this paper is the product of four decades of research into the sources of these mechanisms, at least one of which is a direct consequence of the non-linear terms of the Navier-Stokes equation. A scheme utilizing chaotic dynamic effects that become dominant only for sufficiently high Reynolds numbers is explored. This paper is designed to be of interest to faculty in the engineering, chemistry, physics, biology and mathematics disciplines as well as to practitioners in these and related applications.

ON THE ASYMPTOTIC ANALYSIS OF THE BGK MODEL TOWARD THE INCOMPRESSIBLE LINEAR NAVIER–STOKES EQUATION

2010 ◽  
Vol 20 (08) ◽  
pp. 1299-1318 ◽  
Author(s):  
A. BELLOUQUID
Keyword(s):  
Asymptotic Analysis ◽  
Stokes Equations ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Uniqueness Theorems ◽  
Bgk Model ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Stokes Systems ◽  
Global Strong Solutions

This paper deals with the analysis of the asymptotic limit for BGK model to the linearized Navier–Stokes equations when the Knudsen number ε tends to zero. The uniform (in ε) existence of global strong solutions and uniqueness theorems are proved for regular initial fluctuations. As ε tends to zero, the solution of BGK model converges strongly to the solution of the linearized Navier–Stokes systems. The validity of the BGK model is critically analyzed.

Large-frequency global regularity for the incompressible Navier–Stokes equation

1999 ◽  
Vol 129 (5) ◽  
pp. 903-912
Author(s):  
Joel D. Avrin
Keyword(s):  
Boundary Conditions ◽  
Global Regularity ◽  
Stokes Equations ◽  
Strong Solutions ◽  
Dirichlet Boundary Conditions ◽  
Navier Stokes ◽  
Thin Domains ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Incompressible Navier Stokes Equation

We obtain global existence and regularity of strong solutions to the incompressible Navier–Stokes equations for a variety of boundary conditions in such a way that the initial and forcing data can be large in the high-frequency eigenspaces of the Stokes operator. We do not require that the domain be thin as in previous analyses. But in the case of thin domains (and zero Dirichlet boundary conditions) our results represent a further improvement and refinement of previous results obtained.

A Comparison Between Full and Simplified Navier-Stokes Equation Solutions for Rotating Blade Cascade Flow on S1 Stream Surface of Revolution

1985 ◽  
Author(s):  
Chen Naixing ◽  
Zhang Fengxian
Keyword(s):  
Stokes Equation ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Stream Surface ◽  
Surface Of Revolution ◽  
Rotating Blade ◽  
Blade Cascade ◽  
Cascade Flow

A method for solving the Navier-Stokes equations of the rotating blade cascade flow on S1 stream surface of revolution is developed in the present paper. In this paper a complete set of full and simplified Navier-Stokes equations is given which includes stream-function equation, energy equation and entropy equation, equation of state for a perfect gas, formula for estimating density and formulas for calculating viscous forces, work done by viscous force, dissipation function and heat-transfer term. A comparison between the full and the simplified Navier-Stokes equations is made. The viscous terms of both full and simplified Navier-Stokes equation solutions are also compared in the present paper. The comparison shows that the simplified Navier-Stokes equations are applicable.

THE HYDRODYNAMICS OF ATOMS OF SPACETIME: GRAVITATIONAL FIELD EQUATION IS NAVIER–STOKES EQUATION

2011 ◽  
Vol 20 (14) ◽  
pp. 2817-2822 ◽  
Author(s):  
T. PADMANABHAN
Keyword(s):  
Gravitational Field ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Field Equations ◽  
Gravitational Field Equation ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Gravitational Field Equations ◽  
Conceptual Status ◽  
Null Surface

There is considerable evidence to suggest that field equations of gravity have the same conceptual status as the equations of hydrodynamics or elasticity. We add further support to this paradigm by showing that Einstein"s field equations are identical in form to Navier–Stokes equations of hydrodynamics, when projected on to any null surface. In fact, these equations can be obtained directly by extremizing of entropy associated with the deformations of null surfaces thereby providing a completely thermodynamic route to gravitational field equations. Several curious features of this remarkable connection (including a phenomenon of "dissipation without dissipation") are described and the implications for the emergent paradigm of gravity is highlighted.

scholarly journals Random attractors for stochastic 2D-Navier–Stokes equations in some unbounded domains

2013 ◽  
Vol 255 (11) ◽  
pp. 3897-3919 ◽  
Author(s):  
Z. Brzeźniak ◽  
T. Caraballo ◽  
J.A. Langa ◽  
Y. Li ◽  
G. Łukaszewicz ◽  
...  
Keyword(s):  
Stokes Equations ◽  
Unbounded Domains ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Random Attractors
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