1988
DOI: 10.1007/978-1-4684-0313-8 View full text |Buy / Rent full text
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Abstract: S.A.), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandis… Show more

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“…[12]) The same argument applies to the 3D equations, provided that one assumes regularity (in the sense of Constantin et al [7]), although in this case the estimate of the dimension of the attractor and hence of the number of nodes is much larger (see [7,58] or [26]). …”
Section: The 2d Navier-stokes Equationsmentioning
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“…[12]) The same argument applies to the 3D equations, provided that one assumes regularity (in the sense of Constantin et al [7]), although in this case the estimate of the dimension of the attractor and hence of the number of nodes is much larger (see [7,58] or [26]). …”
Section: The 2d Navier-stokes Equationsmentioning
“…We will compare this to the classical, heuristic, length scale estimates due to [37] (see also [58]; Doering and Gibbon [12] give a much more detailed discussion of such length scales, and Eden et al [13] give a very good summary of the various bounds). Kraichnan's theory constructs a length scale from the viscous enstrophy dissipation and the forcing.…”
Section: The 2d Navier-stokes Equationsmentioning
“…The function u^ + l^ satisfies an équation of the form Then, using the induction assumption (A.2) y , we can apply the uniform Gronwall Lemma (see [14] for instance) to (A.4) and this gives successively …”
Section: The Approximate Manifold Jt Amentioning
“…Nevertheless, it can supply a technical-minded mathematician with a number of new and interesting problems of mathematical nature. There are some results such as steady-state control, stability analysis, robust control of pulse-width sampler systems [1][2][3][4][5][6][7][8][9], integral control by variable sampling based on steady-state data and adaptive sampled-data integral control [10][11][12][13][14][15].…”
Section: Introductionmentioning