Abstract
In this paper, we prove that the 2D Navier-Stokes equations possess a global attractor in H k(Ω, R 2) for any k ≥ 1, which attracts any bounded set of H k(Ω, R 2) in the H k-norm. The result is established by means of an iteration technique and regularity estimates for the linear semigroup of operator, together with a classical existence theorem of global attractor. This extends Ma, Wang and Zhong’s conclusion.
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Supported by the NSF of China (Nos. 10571142, 10771167)
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Di Zhang, Y., Song, L.Y. & Ma, T. The existence of global attractors for 2D Navier-Stokes equations in H k spaces. Acta. Math. Sin.-English Ser. 25, 51–58 (2009). https://doi.org/10.1007/s10114-008-6594-5
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DOI: https://doi.org/10.1007/s10114-008-6594-5