UNSPECIFIED (2003) Low dimensional attractors arise from forcing at small scales. PHYSICA D-NONLINEAR PHENOMENA, 181 (1-2). pp. 39-44. ISSN 0167-2789

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Abstract

Standard estimates of the dimension of the attractor of the 2D Navier-Stokes equations are given in terms of a dimensionless Grashof number that measures the total amount of energy injected into the flow. However, this result takes no I account of whether the forcing is concentrated at large or small scales. By a simple modification of the usual argument, this paper provides a bound that is linear in a modified Grashof number that reflects the spatial structure of the forcing. In particular, as a fixed amount of energy is injected at progressively smaller scales then the dimension of the attractor decreases. (C) 2003 Elsevier Science B.V. All rights reserved.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
Journal or Publication Title:	PHYSICA D-NONLINEAR PHENOMENA
Publisher:	ELSEVIER SCIENCE BV
ISSN:	0167-2789
Date:	1 July 2003
Volume:	181
Number:	1-2
Number of Pages:	6
Page Range:	pp. 39-44
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/9600

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