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
Published electronically: March 22, 2005
MathSciNet review: 2146214
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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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Y. Charles Li
Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
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.