Abstract
We give a simple proof that projecting the 2d Navier-Stokes equations to sufficiently many eigenfunctions of the Stokes operator leads to a system of delayed ODEs. The proof is based on the repeated use of the so-called squeezing property. The reduced system is uniquely solvable and dissipative. Moreover, the solutions on the attractor to the full NSEs are in one-to-one correspondence to the solutions on a compact, invariant subset to a global attractor of the reduced system.
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© 2005 Birkhäuser Verlag Basel/Switzerland
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Pražák, D. (2005). On Reducing the 2d Navier-Stokes Equations to a System of Delayed ODEs. In: Brezis, H., Chipot, M., Escher, J. (eds) Nonlinear Elliptic and Parabolic Problems. Progress in Nonlinear Differential Equations and Their Applications, vol 64. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7385-7_23
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DOI: https://doi.org/10.1007/3-7643-7385-7_23
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-7266-8
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