Theorems about the attractor for incompressible non-Newtonian flow driven by external forces that are rapidly oscillating in time but have a smooth average

This paper discusses the incompressible non-Newtonian fluid with rapidly oscillating external forces g(x,t)=g(x,t,t/) possessing the average g⁰(x,t) as →0⁺, where 0<₀<1. Firstly, with assumptions (A₁)–(A₅) on the functions g(x,t,ξ) and g⁰(x,t), we prove that the Hausdorff distance between the uniform attractors and in space H, corresponding to the oscillating equations and the averaged equation, respectively, is less than O() as →0⁺. Then we establish that the Hausdorff distance between the uniform attractors and in space V is also less than O() as →0⁺. Finally, we show for each [0,₀].     

Random attractor for a two-dimensional incompressible non-Newtonian fluid with multiplicative noise

This article proves that the random dynamical system generated by a twodimensional incompressible non-Newtonian fluid with multiplicative noise has a global random attractor, which is a random compact set absorbing any bounded nonrandom subset of the phase space.     

Existence of the uniform trajectory attractor for a 3D incompressible non-Newtonian fluid flow

This paper studies the trajectory asymptotic behavior of a non-autonomous incompressible non-Newtonian fluid in 3D bounded domains. In appropriate topologies, the authors prove the existence of the uniform trajectory attractor for the translation semigroup acting on the united trajectory space.     

Trajectory attractor and global attractor for a two-dimensional incompressible non-Newtonian fluid

The authors construct the trajectory attractor and global attractor for an autonomous two-dimensional non-Newtonian fluid.     

Determining nodes of the global attractor for an incompressible non-Newtonian fluid

This paper estimates the finite number of the determining nodes to the equations for an incompressible non-Newtonian fluid with space-periodic or no-slip boundary conditions. The authors prove that, whenever the second order derivatives of two different solutions within the global attractor have the same time-asymptotic behavior at finite number of points in the physical space, then the two solutions possess the same time-asymptotic behavior at almost everywhere points of the physical space.     

H 4-boundedness of pullback attractor for a 2D non-Newtonian fluid flow

We prove the H4-boundedness of the pullback attractor for a two- dimensional non-autonomous non-Newtonian fluid in bounded domains.     

Uniform exponential attractor for nonautonomous partly dissipative lattice dynamical system

In this paper,we consider the existence of a uniform exponential attractor for the nonautonomous partly dissipative lattice dynamical system with quasiperiodic external forces.     

一类非牛顿流弱解的扰动

主要研究一类可压缩粘性非牛顿流方程弱解的扰动性质.在已知弱解存在的基础上,证明了选取适当范数时,沿着给定的时间序列,密度和速率的扰动趋于零.     

Nonexistence results for a compressible non-Newtonian fluid with magnetic effects in the whole space

We consider a generalization of the compressible barotropic Navier-Stokes equations to the case of non-Newtonian fluid in the whole space. The viscosity tensor is assumed to be coercive with an exponent q>1. We prove that if the total mass and momentum of the system are conserved, then one can find a constant qγ>1 depending on the dimension of space n and the heat ratio γ such that for q∈[qγ,n) there exists no global in time smooth solution to the Cauchy problem. We prove also an analogous result for solutions to equations of magnetohydrodynamic non-Newtonian fluid in 3D space.     

Attractors for non-autonomous wave equations with a new class of external forces

We introduce a new concept Condition (C*), and denote the set of all functions satisfying Condition (C*) by , which are translation bounded but not translation compact in , and we show that there are many functions satisfying Condition (C*); then, in application, we obtain the existence of uniform attractors in for non-autonomous wave equations involving mixed differential quotient terms with this new class of time dependent external forces .     

Uniform attractor for non‐autonomous Boussinesq‐type equation with critical nonlinearity

In this paper, we study the longtime dynamics of the non‐autonomous Boussinesq‐type equation with critical nonlinearity, and time‐dependent external forcing, which is translation bounded but not translation compact. We prove the existence of a uniform attractor in . Copyright © 2015 John Wiley & Sons, Ltd.     

Global attractor for heat convection problem in a micropolar fluid

The article is devoted to describe asymptotics in the heat convection problem for a micropolar fluid in two dimensions. We show the existence and the uniqueness of global in time solutions and then prove the existence of a global attractor for considered model. Next, the Hausdorff dimension of the global attractor is estimated. Copyright © 2006 John Wiley & Sons, Ltd.     

Uniform attractor for non‐autonomous suspension bridge equations with localized damping

In this paper, we prove the existence of a uniform attractor for non‐autonomous suspension bridge equations with localized damping. Copyright © 2010 John Wiley & Sons, Ltd.     

Global periodic attractor of a class of third-order phase-locked loop

The uniform boundedness and existence of a global periodic attractor for a third-order phase-locked loop with general phase detector characteristics and frequency modulation input is proved under some parametric conditions. Project supported by the National Natural Science Foundation of China.     

Ladder estimates for micropolar fluid equations and regularity of global attractor

This paper is devoted to obtain ladder inequalities for 2D micropolar fluid equations on a periodic domain Q=(0, L)². The ladder inequalities are differential inequalities that connect the evolution of L² norms of derivatives of order N with the evolution of the L² norms of derivatives of other (usually lower) order. Moreover, we find (with slight assumption on external fields) long‐time upper bounds on the L² norms of derivatives of every order, which implies that a global attractor is made up from C^∞ functions. Copyright © 2010 John Wiley & Sons, Ltd.     

One method for constructing exact solutions of equations of two-dimensional hydrodynamics of an incompressible fluid

We propose a simple algebraic method for constructing exact solutions of equations of two-dimensional hydrodynamics of an incompressible fluid. The problem reduces to consecutively solving three linear partial differential equations for a nonviscous fluid and to solving three linear partial differential equations and one first-order ordinary differential equation for a viscous fluid. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 147,No. 1, pp. 64–72, April, 2006.     

Uniform attractors for a nonautonomous extensible plate equation with a strong damping

In this paper, we study the long‐time dynamics of solutions to a nonlinear nonautonomous extensible plate equation with a strong damping. Under some suitable assumptions on the initial data, the nonlinear term and external force, we establish the existence of global solutions that generate a family of processes for the problem and obtain uniform attractors corresponding to strong and weak symbol spaces in a bounded domain . Copyright © 2016 John Wiley & Sons, Ltd.     

Global attractor for a class of nonlinear lattices

We consider a class of nonlinear lattices with nonlinear damping

(0.1)     

Uniform attractor for non-autonomous plate equation with a localized damping and a critical nonlinearity

In this paper, we consider dynamical behavior of non-autonomous plate-type evolutionary equations with critical nonlinearity. We prove the existence of a uniform attractor in the space .