Damping-Diffusion-Noise Interactions in the Stochastic Camassa--Holm Equation
Analysis of PDEs
2024-10-11 v1
Abstract
We investigate the effects of the interaction between time-inhomogeneous damping, non-local diffusion, and noise on classical solutions to the Camassa--Holm equations that incorporate these additional factors. Initially, a local-in-time theory is developed, covering the existence, uniqueness, and a blow-up criterion under relatively general conditions for these interacting factors. Subsequently, we identify different conditions on the interactions between damping, diffusion, and noise that enable the global regularity and long-time behaviour of classical solutions. Notably, we demonstrate the existence of an evolution system of measures, generalising the concept of invariant measures to the time-inhomogeneous system.
Cite
@article{arxiv.2410.07649,
title = {Damping-Diffusion-Noise Interactions in the Stochastic Camassa--Holm Equation},
author = {Diego Alonso-Orán and Peter H. C. Pang and Hao Tang},
journal= {arXiv preprint arXiv:2410.07649},
year = {2024}
}