Abstract
In this paper, we present a basic theoretical framework for interpreting essentially all known methods for constructing approximate inertial manifolds for any of a large class of nonlinear evolutionary equations. This class includes the 2D Navier-Stokes equations and many systems of reaction diffusion equations. We prove that, under reasonable assumptions, every approximate inertial manifold for a given equation is an actual inertial manifold of an approximate equation. This new theoretical framework allows one to introduce certain optimality conditions for approximate inertial manifolds. Finally we introduce a new method, the Gamma Method, for the construction of approximate inertial manifolds.
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This research was supported in part by grants from the National Science Foundation, the Applied Mathematics and Computational Mathematics Program/DARPA, and the U. S. Army.
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© 1993 Springer-Verlag New York, Inc.
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Sell, G.R. (1993). An Optimality Condition for Approximate Inertial Manifolds. In: Sell, G.R., Foias, C., Temam, R. (eds) Turbulence in Fluid Flows. The IMA Volumes in Mathematics and its Applications, vol 55. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4346-5_10
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DOI: https://doi.org/10.1007/978-1-4612-4346-5_10
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