Ergodic isospectral theory of the Lax pairs of Euler equations with harmonic analysis flavor

Author:
Y. Charles Li

Journal:
Proc. Amer. Math. Soc. **133** (2005), 2681-2687

MSC (2000):
Primary 35P05, 46N20, 76B99; Secondary 37A30, 42A99

DOI:
https://doi.org/10.1090/S0002-9939-05-07828-7

Published electronically:
March 22, 2005

MathSciNet review:
2146214

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Abstract | References | Similar Articles | Additional Information

Abstract: Isospectral theory of the Lax pairs of both 3D and 2D Euler equations of inviscid fluids is developed. Eigenfunctions are represented through an ergodic integral. The Koopman group and mean ergodic theorem are utilized. Further harmonic analysis results on the ergodic integral are introduced. The ergodic integral is a limit of the oscillatory integral of the first kind.

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Additional Information

**Y. Charles Li**

Affiliation:
Department of Mathematics, University of Missouri, Columbia, Missouri 65211

Email:
cli@math.missouri.edu

DOI:
https://doi.org/10.1090/S0002-9939-05-07828-7

Keywords:
Lax pair,
Euler equation,
ergodic theorem,
oscillatory integral,
isospectral theory

Received by editor(s):
March 12, 2004

Received by editor(s) in revised form:
April 23, 2004

Published electronically:
March 22, 2005

Communicated by:
Carmen C. Chicone

Article copyright:
© Copyright 2005
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.