Wave turbulence for the BBM equation : Stability of a Gaussian statistics under the flow of BBM
Anne-Sophie de Suzzoni
TL;DR
This paper investigates the stability of Gaussian statistical measures under the flow of the BBM equation within the wave turbulence framework, highlighting invariance properties and perturbation effects.
Contribution
It introduces an invariant measure for the BBM equation and analyzes its stability under specific perturbations, advancing wave turbulence theory.
Findings
Gaussian measures are invariant under BBM flow
Stability of these measures is established for certain perturbations
Results contribute to understanding wave turbulence in nonlinear dispersive equations
Abstract
This paper introduces a measure or statistics invariant through the flow of the Benjamin-Bona-Mahony equation and studies its stability, regarding a specific class of perturbation and in the idea of the wave turbulence theory.
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