Attractors for nonautonomous Navier-Stokes system and other partial differential equations. (English) Zbl 1141.76018
Bardos, Claude (ed.) et al., Instability in models connected with fluid flows I. New York, NY: Springer (ISBN 978-0-387-75216-7/hbk). International Mathematical Series (New York) 6, 135-265 (2008).
Summary: We present general methods for constructing and studying global attractors of nonautonomous evolution partial differential equations. The nonautonomous 2D Navier-Stokes system with time-dependent external force serves as the main example. The Kolmogorov \(\varepsilon\)-entropy and fractal dimension of global attractors are considered for this system and for other important equations of mathematical physics. We also establish the convergence of global attractors of nonautonomous equations with singularly oscillating terms to attractors of the corresponding “limit” equations.
For the entire collection see [Zbl 1130.76003].
For the entire collection see [Zbl 1130.76003].
MSC:
| 76D03 | Existence, uniqueness, and regularity theory for incompressible viscous fluids |
| 35Q30 | Navier-Stokes equations |
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