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On the embedding of the attractor generated by Navier-Stokes equations into finite dimensional spaces


Author: Mahdi Mohebbi
Journal: Proc. Amer. Math. Soc. 141 (2013), 3453-3465
MSC (2010): Primary 37L30; Secondary 54C25
Published electronically: June 10, 2013
MathSciNet review: 3080168
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Abstract: For 2-D Navier-Stokes equations on a $ C^2$ bounded domain $ \Omega $, a class of nonlinear homeomorphisms is constructed from the attractor of Navier-Stokes to curves in $ \mathbb{R}^N$ for sufficiently large $ N$. The construction uses an $ \varepsilon $-net on $ \Omega $ (so does not use the information ``near'' the boundary) and is more physically perceivable compared to abstract common embeddings.


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Additional Information

Mahdi Mohebbi
Affiliation: Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, Pennsylvania 15261
Email: mam175@pitt.edu

DOI: https://doi.org/10.1090/S0002-9939-2013-11618-7
Received by editor(s): May 24, 2011
Received by editor(s) in revised form: October 3, 2011, and December 8, 2011
Published electronically: June 10, 2013
Additional Notes: This work was partially supported by NSF grant DMS-1062381.
Communicated by: Walter Craig
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.