Pullback Attractors for Nonautonomous 2D-Navier-Stokes Models with Variable Delays
نویسنده
چکیده
and Applied Analysis 3 Theorem 4 (see [21, 22]). Let X,Y be two Banach spaces satisfy the previous assumptions, and let {U(t, τ)} be amultivalued process onX andY, respectively. Assume that {U(t, τ)} is upper semicontinuous or weak upper semicontinuous on Y. If for fixed t ⩾ τ, τ ∈ R, U(t, τ) maps compact subsets of X into bounded subsets ofP(X), then U(t, τ) is norm-to-weak upper semicontinuous onX. By slightly modifying the arguments of Theorem 3.4 and Remark 3.9 in [21], we have the following. Theorem 5. Let X be a Banach space, and let {U(t, τ)} be a multivalued process on X. Also let U(t, τ)x be norm-to-weak upper semicontinuous in x for fixed t ⩾ τ, τ ∈ R; that is, if x n → x, then for any y n ∈ U(t, τ)x n , there exist a subsequence y n k ∈ U(t, τ)x n k and a y ∈ U(t, τ)x such that y n k ⇀ y (weak convergence). Then the multivalued process {U(t, τ)} possesses a pullbackD-attractorA = {A(t)} t∈R inX given by
منابع مشابه
Pullback attractors for three-dimensional Navier-Stokes-Voigt equations with delays
*Correspondence: [email protected] 2Department of Applied Mathematics, Donghua University, Shanghai, 201620, P.R. China Full list of author information is available at the end of the article Abstract Our aim in this paper is to study the existence of pullback attractors for the 3D Navier-Stokes-Voigt equations with delays. The forcing term g(t,u(t – ρ(t))) containing the delay is sub-linea...
متن کاملThe 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 alm...
متن کاملUpper Semicontinuity of Pullback Attractors for Non-autonomous Generalized 2d Parabolic Equations
This paper is concerned with a generalized 2D parabolic equation with a nonautonomous perturbation −∆ut + α ∆ut + μ∆ u+∇ · −→ F (u) +B(u, u) = ǫg(x, t). Under some proper assumptions on the external force term g, the upper semicontinuity of pullback attractors is proved. More precisely, it is shown that the pullback attractor {Aǫ(t)}t∈R of the equation with ǫ > 0 converges to the global attract...
متن کاملAttractors for Noncompact Nonautonomous Systems via Energy Equations
An extension to the nonautonomous case of the energy equation method for proving the existence of attractors for noncompact systems is presented. A suitable generalization of the asymptotic compactness property to the nonautonomous case, termed uniform asymptotic compactness, is given, and conditions on the energy equation associated with an abstract class of equations that assure the uniform a...
متن کامل