Dynamical behaviour of non-autonomous 2D Navier-Stokes equations with singularly oscillating external force

• Published in: Dynamical systems (London, England) Vol. 26; no. 3; pp. 245 - 260
• Main Author: Yan, Xingjie
• Format: Journal Article
• Language: English
• Published: Taylor & Francis Group 01-09-2011
• Subjects: averaging; Divergence; Dynamical systems; Mathematical analysis; Navier-Stokes equation; Navier-Stokes equations; Oscillating; Two dimensional; uniform attractor
• ISSN: 1468-9367; 1468-9375
• DOI: 10.1080/14689367.2011.572063

The purpose of this article is to analyse the dynamical behaviour of solutions of the non-autonomous 2D Navier-Stokes equations with singularly oscillating external force of the form:
. First, we prove the existence of uniform attractor
in
for equations with external force non-translation compact. Then we prove that if the function g
1
(z, t) satisfies the Divergence condition (Definition 3.1), then the uniform attractor
is convergent to uniform attractor
of the averaged equations in the sense of Hausdorff distance in L
2
(Ω).