2009
DOI: 10.1016/j.na.2009.02.107
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Attractors for nonautonomous 2D Navier–Stokes equations with less regular symbols

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Cited by 14 publications
(11 citation statements)
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“…In our theorem, we assume that the external force g ∈ L ∞ (R, L 2 (Ω)) and g t ∈ L 2 b (R; L 2 (Ω)), this means g(t, x) is translation compact from Lemma 4.1 and 4.2. Using more optimal conditions such as translation bounded, normal class in [14], [16], [15], [19], [18], [17] and [28], we can obtain the existence of weak uniform attractor A w in less regular phase space, which has some relation with the strong one A. Definition 7.1.…”
Section: It Follows From Theorem 22 Thatmentioning
confidence: 99%
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“…In our theorem, we assume that the external force g ∈ L ∞ (R, L 2 (Ω)) and g t ∈ L 2 b (R; L 2 (Ω)), this means g(t, x) is translation compact from Lemma 4.1 and 4.2. Using more optimal conditions such as translation bounded, normal class in [14], [16], [15], [19], [18], [17] and [28], we can obtain the existence of weak uniform attractor A w in less regular phase space, which has some relation with the strong one A. Definition 7.1.…”
Section: It Follows From Theorem 22 Thatmentioning
confidence: 99%
“…(4) Originated by the idea in [4], [9], the uniform attractor can be achieved, which require the external forces is translation compact. One natural question is what's the sharp condition for external forces, which has been solved in [14], [16], [15], [17], [18], [19], and improved by [28]. Inspired by [28], we use the time or space regular functions class to conclude the relation between weak and strong uniform attractors.…”
mentioning
confidence: 99%
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“…The most known example here is the so-called normal external forces which usually give the strong compactness in the case of parabolic PDEs in bounded domains, see [1,12,13] and Sections 3 and 5 for more details. Mention also the paper [15] where the weaker than normal class of external forces (which is close to the necessary one to have the strong attractor) is introduced, see also Section 1.…”
Section: Introductionmentioning
confidence: 99%
“…If the nonlinearity term f is independent of t, then the nonautonomous term is only about the external time-dependent force g. In this case, if g is translation compact in L loc 2 (R; L 2 (Ω)), as a special case in [3], the authors obtained the uniform attractor A for reaction-diffusion equations, as well as Navier-Stokes equations in L 2 (Ω) and for hyperbolic equations in H 1 0 ×L 2 (Ω), and described the structure of A by showing the continuity of the skew-product dynamical system. Later on, there are many literatures [10], [8], [9], [13], [11], [12], [20], devoted to finding wider classes of the admissible force g with compactness of symbol space in only weak convergence topology space, for example, g is only normal, not translation compact. Recently, [19] proved the existence of uniform attractors for plate equation with p-Laplacian perturbation.…”
mentioning
confidence: 99%