Structure Of Uniform Attractor Research Articles

Attractors for nonautonomous 2D Navier–Stokes equations with less regular normal forces

First, the existence and structure of uniform attractors in H is proved for nonautonomous 2D Navier–Stokes equations on bounded domain with a new class of distribution forces, termed normal in L loc 2 ( R ; V ′ ) (see Definition 3.1), which are translation bounded but not translation compact in L loc 2 ( R ; V ′ ) . Then, the properties of the kernel section are investigated. Last, the fractal dimension is estimated for the kernel sections of the uniform attractors obtained.

Uniform Attractors for Nonautonomous Wave Equations with Nonlinear Damping

We consider dynamical behavior of nonautonomous wave‐type evolutionary equations with nonlinear damping, critical nonlinearity, and time‐dependent external forcing which is translation bounded but not translation compact (i.e., external forcing is not necessarily time‐periodic, quasi‐periodic, or almost periodic). A sufficient and necessary condition for the existence of uniform attractors is established using the concept of uniform asymptotic compactness. A new method for verifying uniform asymptotic compactness is devised. The required compactness for the existence of uniform attractors is then fulfilled by some new a priori estimates for concrete wave‐type equations arising from applications. The structure of uniform attractors is obtained by constructing a skew product flow on the extended phase space.

Uniform attractors for nonautonomous incompressible non-Newtonian fluid with locally uniform integrable external forces

This paper discusses the long time behavior of solutions for a two-dimensional (2D) nonautonomous incompressible non-Newtonian fluid in 2D bounded domains. When the external force g0(x,t) is locally uniform integrable (see Definition 1.1) in Lloc2(R;H), the authors obtain the existence and structure of uniform attractors in space V for the family of processes associated with the fluid. Moreover, when ∥g0∥Lb2 is properly small, they provide some interesting corollaries.

Attractors for nonautonomous 2d Navier-Stokes equations with normal external forces

The existence and structure of uniform attractors in $V$ is proved for nonautonomous 2D Navier-stokes equations on bounded domain with a new class of external forces, termed normal in $L_{l o c}^2(\mathbb R; H)$ (see Definition 3.1), which are translation bounded but not translation compact in $L_{l o c}^2(\mathbb R; H)$. To this end, some abstract results are established. First, a characterization on the existence of uniform attractor for a family of processes is presented by the concept of measure of noncompactness as well as a method to verify it. Then, the structure of the uniform attractor is obtained by constructing skew product flow on the extended phase space with weak topology. Finally, the uniform attractor of a process is identified with that of a family of processes with symbols in the closure of the translation family of the original symbol in a Banach space with weak topology.

On the Structure of Uniform Attractors

On the Structure of Uniform Attractors