The Pullback Attractors for the Nonautonomous Camassa-Holm Equations

The Pullback Attractors for the Nonautonomous Camassa-Holm Equations

Finite Dimensional Uniform Attractors for the Nonautonomous Camassa-Holm Equations

and Applied Analysis 3 and in H1 Ω , respectively, observe that H⊥, the orthogonal complement of H in L2 Ω , is {∇p : p ∈ H1 Ω } cf. 11 or 12 . ii We denote P : L2 Ω 3 → H the L2 orthogonal projection, usually referred as Helmholtz-Leray projector, and by A −PΔ the Stokes operator with domain D A H2 Ω 3 ∩ V . Notice that in the case of periodic boundary condition, A −Δ|D A is a selfadjoint posi...

Pullback attractors of nonautonomous reaction–diffusion equations

In this paper, firstly we introduce the concept of norm-to-weak continuous cocycle in Banach space and give a technical method to verify this kind of continuity, then we obtain some abstract results for the existence of pullback attractors about this kind of cocycle, using the measure of noncompactness. As an application, we prove the existence of pullback attractors in H 1 0 of the cocycle ass...

Attractors for the Viscous Camassa-holm Equation

Abstract. We consider the viscous Camassa-Holm equation subject to an external force, where the viscosity term is given by second order differential operator in divergence form. We show that under some mild assumptions on the viscosity term, one has global wellposedness both in the periodic case and the case of the whole line. In the periodic case, we show the existence of global attractors in ...

Pullback Exponential Attractors for Nonautonomous Reaction-Diffusion Equations

Under the assumption that g t ( ) is translation bounded in loc L R L 4 4 ( ; ( )) Ω , and using the method developed in [3], we prove the existence of pullback exponential attractors in H 1 0 ( ) Ω for nonlinear reaction diffusion equation with polynomial growth nonlinearity( p 2 ≥ is arbitrary).