Pullback attractors of 2D Navier-Stokes equations with weak damping and continuous delay

• Published in: Boundary value problems Vol. 2015; no. 1; p. 1
• Main Authors: Li, Juntao, Wang, Yadi, Yang, Xin-Guang
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 21.05.2015; Hindawi Limited
• Subjects: Analysis; Approximations and Expansions; Boundary value problems; Difference and Functional Equations; Mathematics; Mathematics and Statistics; Navier-Stokes equations; Ordinary Differential Equations; Partial Differential Equations; Navier-Stokes equation with weak damping; continuous delay; pullback attractors
• ISSN: 1687-2770; 1687-2762; 1687-2770
• DOI: 10.1186/s13661-015-0344-2

In this present paper, the existence of pullback attractors for the 2D Navier-Stokes equation with weak damping and continuous delay is considered; by virtue of the classical Galerkin method, we derive the existence and uniqueness of global weak and strong solutions. Using the Aubin-Lions lemma and some energy estimate in the Banach space with delay, we obtain the uniform bound and the existence of a uniform pullback absorbing ball for the solution’s semi-processes, and we conclude to the global attractors via verifying the pullback asymptotical compactness by the generalized Arzelà-Ascoli theorem.