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Abstract We prove an analytic version of the stable graph regularity lemma by Malliaris and Shelah (Trans. Amer. Math. Soc.366(2014), no. 3, 1551–1585), which applies to stable functions . Our methods involve continuous model theory and, in particular, results on the structure of local Keisler measures for stable continuous formulas. Along the way, we develop some basic tools around ultraproducts of metric structures and linear functionals on continuous formulas, and we also describe several concrete families of examples of stable functions.
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Islands in stable fluid equilibria
We prove that stable fluid equilibria with trivial homology on curved, reflection-symmetric periodic channels must posses “islands”, or cat’s eye vortices. In this way, arbitrarily small disturbances of a flat boundary cause a change of streamline topology of stable steady states.
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- Award ID(s):
- 2235395
- PAR ID:
- 10576882
- Publisher / Repository:
- AMS
- Date Published:
- Journal Name:
- Proceedings of the American Mathematical Society
- Volume:
- 152
- Issue:
- 785
- ISSN:
- 0002-9939
- Page Range / eLocation ID:
- 4855 to 4863
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript
- Journal Article:
- https://doi.org/10.1090/proc/16951
