Non-autonomous Navier-Stokes Equations Research Articles

Random pullback and uniform exponential attractors for stochastic non-autonomous Navier-Stokes equations

We first prove the existence of a random pullback exponential attractor for the 2D Navier-Stokes equation with additive noise and non-autonomous forcing. Then, we introduce the definition and existence conditions of a random uniform exponential attractor for a jointly continuous non-autonomous random dynamical system, and prove the existence of a random uniform exponential attractor for the 2D Navier-Stokes equation with additive noise and quasi-periodic external forces.

Dynamics of 2D Incompressible Non-autonomous Navier–Stokes Equations on Lipschitz-like Domains

This paper concerns the tempered pullback dynamics of 2D incompressible non-autonomous Navier–Stokes equations with a non-homogeneous boundary condition on Lipschitz-like domains. With the presence of a time-dependent external force f(t) which only needs to be pullback translation bounded, we establish the existence of a minimal pullback attractor with respect to a universe of tempered sets for the corresponding non-autonomous dynamical system. We then give estimates on the finite fractal dimension of the attractor based on trace formula. Under the additional assumption that the external force is perturbed from a stationary force by a time-dependent perturbation, we also prove the upper semi-continuity of the attractors as the non-autonomous perturbation vanishes. Lastly, we investigate the regularity of these attractors when smoother initial data are given. Our results are new even for smooth domains.

Pullback exponential attractors for the three dimensional non-autonomous Navier-Stokes equations with nonlinear damping

The main objective of this paper is to study the long-time behavior of solutions for the three dimensional non-autonomous Navier-Stokes equations with nonlinear damping for $ r>4. $ Inspired by the the methods of $ \ell $-trajectories in [27], we will prove the existence of a finite dimensional pullback attractor and a pullback exponential attractor, which gives another way of considering the long-time behavior of the non-autonomous evolutionary equations.

The long-time dynamics of 3D non-autonomous Navier-Stokes equations with variable viscosity

The long-time dynamics of 3D non-autonomous Navier-Stokes equations with variable viscosity

Pullback Dynamics of 2D Non-autonomous Navier-Stokes Equations with Klein-Voight Damping and Multi-delays

Pullback Dynamics of 2D Non-autonomous Navier-Stokes Equations with Klein-Voight Damping and Multi-delays

Cauchy problem for non-autonomous Navier-Stokes equations in an unbounded domain

This paper concerns the global existence of solutions to a system of non-linear compressible non-autonomous Navier–Stokes equations in an unbounded domain. To prove the global existence, we first study an approximate problem in a bounded domain and obtain a priori estimates independent of the boundary of the domain. Then letting the diameter of the domain tend to infinity, we get a global spherically symmetric solution as the limit.

Upper Semicontinuous Property of Uniform Attractors for the 2D Nonautonomous Navier-Stokes Equations with Damping

Our aim is to investigate the long-time behavior in terms of upper semicontinuous property of uniform attractors for the 2D nonautonomous Navier-Stokes equations with linear damping and nonautonomous perturbation external force, that is, the convergence of corresponding attractors when the perturbation tends to zero.

A remark on uniform attractors for the 2D non-autonomous Navier-Stokes equation with damping

We shall show the existence of uniform attractors for the 2D nonautonomous Navier-Stokes equations with damping by contractive functions method which is more simple than the weak continuous method to establish the uniformly asymptotical compactness in H. Mathenatics Subject Classification: 35Q35; 76D03

The Uniform Attractors for the Nonhomogeneous 2D Navier-Stokes Equations in Some Unbounded Domain

We consider the attractors for the two-dimensional nonautonomous Navier-Stokes equations in some unbounded domain Ω with nonhomogeneous boundary conditions. We apply the so-called uniformly ω-limit compact approach to nonhomogeneous Navier-Stokes equation as well as a method to verify it. Assuming f ∈ Lloc 0, T ;L2 Ω , which is translation compact and φ ∈ C1 b R ;H2 R1 × {±L} asymptotically almost periodic, we establish the existence of the uniform attractor in H1 Ω .

The attractors for the nonhomogeneous nonautonomous Navier–Stokes equations

In this paper, we consider the attractors for the two-dimensional nonautonomous Navier–Stokes equations in nonsmooth bounded domain Ω with nonhomogeneous boundary condition u = φ on ∂ Ω. Assuming f = f ( x , t ) ∈ L loc 2 ( ( 0 , T ) ; D ( A α 4 ) ) , which is translation compact and φ ∈ L ∞ ( ∂ Ω ) , we establish the existence of the uniform attractor in L 2 ( Ω ) and D ( A 1 4 ) .

The uniform attractor for the 2D non-autonomous Navier–Stokes flow in some unbounded domain

By using the energy equation method, the existence of the uniform attractor for the 2D non-autonomous Navier–Stokes equations in some unbounded domains with usual settings is obtained without the restriction of the forcing term belonging to some weighted Sobolev space. And for the quasi-periodic forcing term, the estimation of the Hausdorff dimension of such attractors is also obtained.

Uniform attractor for 2D magneto-micropolar fluid flow in some unbounded domains

We investigate the flow of a magneto-micropolar fluid in an arbitrary unbounded domain on which the Poincare inequality holds. Assuming homogeneous boundary conditions and the external fields to be almost periodic in time we prove the existence of the uniform attractor by using the energy method [10] which we generalize to nonautonomous systems. We consider the problem in an abstract setting that allows to include also other hydrodynamical models. In particular, we extend the result of R. Rosa [12] from autonomous to nonautonomous Navier-Stokes equations in unbounded domains.

Almost Periodic Solutions and Global Attractors of Non-autonomous Navier–Stokes Equations

The article is devoted to the study of non-autonomous Navier-Stokes equations. First, the authors have proved that such systems admit compact global attractors. This problem is formulated and solved in the terms of general non-autonomous dynamical systems. Second, they have obtained conditions of convergence of non-autonomous Navier-Stokes equations. Third, a criterion for the existence of almost periodic (quasi periodic,almost automorphic, recurrent, pseudo recurrent) solutions of non-autonomous Navier-Stokes equations is given. Finally, the authors have derived a global averaging principle for non-autonomous Navier-Stokes equations.