Ergodic Isospectral Theory of the Lax Pairs of Euler Equations with Harmonic Analysis Flavor
نویسنده
چکیده
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.
منابع مشابه
Euler Equations of Inviscid Fluids
Progresses on the dynamical system theory of 2D Euler equation are reported. An open problem is presented. The isospectral theory on Lax pairs of Euler equations is initiated.
متن کاملTrivially related lax pairs of the Sawada-Kotera equation
We show that a recently introduced Lax pair of the Sawada-Kotera equation is nota new one but is trivially related to the known old Lax pair. Using the so-called trivialcompositions of the old Lax pairs with a differentially constrained arbitrary operators,we give some examples of trivial Lax pairs of KdV and Sawada-Kotera equations.
متن کاملSize-Dependent Forced Vibration Analysis of Three Nonlocal Strain Gradient Beam Models with Surface Effects Subjected to Moving Harmonic Loads
The forced vibration behaviors are examined for nonlocal strain gradient nanobeams with surface effects subjected to a moving harmonic load travelling with a constant velocity in terms of three beam models namely, the Euler-Bernoulli, Timoshenko and modified Timoshenko beam models. The modification for nonlocal strain gradient Timoshenko nanobeams is exerted to the constitutive equations by exc...
متن کاملA Novel Method for Considering Interlayer Effects between Graphene Nanoribbons and Elastic Medium in Free Vibration Analysis
A complete investigation on the free vibration of bilayer graphene nanoribbons (BLGNRs) mod-eled as sandwich beams taking into account tensile-compressive and shear effects of van der Waals (vdWs) interactions between adjacent graphene nanoribbons (GNRs) as well as between GNRs and polymer matrix is performed in this research. In this modeling, nanoribbon layers play role of sandwich beam layer...
متن کاملNonlinear Vibration Analysis of Embedded Multiwalled Carbon Nanotubes in Thermal Environment
In this article, based on the Euler-Bernoulli beam theory, the large-amplitude vibration of multiwalled carbon nanotubes embedded in an elastic medium is investigated. The method of incremental harmonic balance is implemented to solve the set of governing nonlinear equations coupled via the van der Waals (vdW) interlayer force. The influences of number of tube walls, the elastic medium, nanotub...
متن کامل