José A Langa and James C Robinson 2001 Nonlinearity 14 673 doi:10.1088/0951-7715/14/4/301
A finite number of point observations which determine a non-autonomous fluid flow
José A Langa1 and James C Robinson2
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We show that a finite number of point observations serve to determine the flow field throughout the entire domain for certain two-dimensional (2D) flows. In particular, we consider the 2D Navier-Stokes equations with periodic boundary conditions and a time-dependent forcing which is analytic in space. Using the theory of non-autonomous attractors developed by Chepyzhov and Vishik, and the theory of point observations developed by Friz and Robinson, we show that almost every choice of a sufficient number of `nodes' in the domain gives an evaluation map u
(u(x1),...,u(xk)) which is one-to-one between the attractor and its image.
- PACS
- MSC
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37L30 Attractors and their dimensions, Lyapunov exponents
76D05 Navier-Stokes equations (See also 35Q30)
35Q30 Stokes and Navier-Stokes equations (See also 76D05, 76D07, 76N10)
- Subjects
- Dates
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Issue 4 (July 2001)
Received 19 June 2000
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A finite number of point observations which determine a non-autonomous fluid flow
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