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Pull-back attractors for three-dimensional Navier—Stokes—Voigt equations in some unbounded domains

Published online by Cambridge University Press:  30 May 2013

Cung The Anh  and
Pham Thi Trang
Cung The Anh
Affiliation:
Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy, Cau Giay, Hanoi, Vietnam (anhctmath@hnue.edu.vn; phamtrangsph@gmail.com)
Pham Thi Trang
Affiliation:
Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy, Cau Giay, Hanoi, Vietnam (anhctmath@hnue.edu.vn; phamtrangsph@gmail.com)
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Abstract

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We study the first initial–boundary-value problem for the three-dimensional non-autonomous Navier–Stokes–Voigt equations in an arbitrary (bounded or unbounded) domain satisfying the Poincaré inequality. The existence of a weak solution to the problem is proved by using the Faedo–Galerkin method. We then show the existence of a unique minimal finite-dimensional pull-back -attractor for the process associated with the problem, with respect to a large class of non-autonomous forcing terms. We also discuss relationships between the pull-back attractor, the uniform attractor and the global attractor.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 143 , Issue 2 , April 2013 , pp. 223 - 251
Copyright
Copyright © Royal Society of Edinburgh 2013