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This article is cited in 33 scientific papers (total in 33 papers)
On convergence of trajectory attractors of the 3D Navier–Stokes-$\alpha$
model as $\alpha$ approaches 0
M. I. Vishika, E. S. Titibc, V. V. Chepyzhova a Institute for Information Transmission Problems, Russian Academy of Sciences
b Weizmann Institute of Science
c University of California, Irvine
Abstract:
We study the relations between the long-time dynamics of the Navier–Stokes-$\alpha$ model
and the exact 3D Navier–Stokes system. We prove that bounded sets of solutions of the Navier–Stokes-$\alpha$ model converge to the trajectory attractor $\mathfrak A_0$ of the
3D Navier–Stokes system as the time approaches infinity and $\alpha$ approaches zero. In particular, we show that the trajectory attractor $\mathfrak A_\alpha$ of the Navier–Stokes-$\alpha$ model converges to the trajectory attractor $\mathfrak A_0$ of the 3D Navier–Stokes system as $\alpha\to0+$. We also construct the minimal limit
$\mathfrak A_{\min}(\subseteq\!\mathfrak A_0)$ of the trajectory
attractor $\mathfrak A_\alpha$ as $\alpha\to0+$ and prove that the
set $\mathfrak A_{\min}$ is connected and strictly invariant.
Bibliography: 35 titles.
Received: 23.01.2007
Citation:
M. I. Vishik, E. S. Titi, V. V. Chepyzhov, “On convergence of trajectory attractors of the 3D Navier–Stokes-$\alpha$
model as $\alpha$ approaches 0”, Mat. Sb., 198:12 (2007), 3–36; Sb. Math., 198:12 (2007), 1703–1736
Linking options:
https://www.mathnet.ru/eng/sm3832https://doi.org/10.1070/SM2007v198n12ABEH003902 https://www.mathnet.ru/eng/sm/v198/i12/p3
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Abstract page: | 1002 | Russian version PDF: | 275 | English version PDF: | 30 | References: | 114 | First page: | 11 |
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