On the embedding of the attractor generated by Navier-Stokes equations into finite dimensional spaces
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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.References
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Additional Information
- Mahdi Mohebbi
- Affiliation: Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, Pennsylvania 15261
- MR Author ID: 1029609
- Email: mam175@pitt.edu
- 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
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 3453-3465
- MSC (2010): Primary 37L30; Secondary 54C25
- DOI: https://doi.org/10.1090/S0002-9939-2013-11618-7
- MathSciNet review: 3080168