Ergodic isospectral theory of the Lax pairs of Euler equations with harmonic analysis flavor
Authors:
Y. Charles Li
Affiliation:
Department of Mathematics, University of Missouri, Columbia, Missouri 65211
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.