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Pullback attractors for three-dimensional Navier-Stokes-Voigt equations with delays

Haiyan Li1 and Yuming Qin2*

Author Affiliations

1 College of Information Science and Technology, Donghua University, Shanghai, 201620, P.R. China

2 Department of Applied Mathematics, Donghua University, Shanghai, 201620, P.R. China

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Boundary Value Problems 2013, 2013:191  doi:10.1186/1687-2770-2013-191

Published: 27 August 2013

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 <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/191/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/191/mathml/M1">View MathML</a> containing the delay is sub-linear and continuous with respect to u. Since the solution of the model is not unique, which is caused by the continuity assumption, we establish the existence of pullback attractors for our problem by using the theory of multi-valued dynamical system.

Keywords:
3D Navier-Stokes-Voigt equations; pullback attractors; delay terms; multi-valued process