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
- MR Author ID: 270213
- Email: firstname.lastname@example.org
- 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
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
- 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
- MathSciNet review: 2146214