Stochastic Camassa-Holm equation with convection type noise
Functional Analysis
2019-11-19 v1 Analysis of PDEs
Abstract
We consider a stochastic Camassa-Holm equation driven by a one-dimensional Wiener process with a first order differential operator as diffusion coefficient. We prove the existence and uniqueness of local strong solutions of this equation. In order to do so, we transform it into a random quasi-linear partial differential equation and apply Kato's operator theory methods. Some of the results have potential to find applications to other nonlinear stochastic partial differential equations.
Keywords
Cite
@article{arxiv.1911.07077,
title = {Stochastic Camassa-Holm equation with convection type noise},
author = {Sergio Albeverio and Zdzisław Brzeźniak and Alexei Daletskii},
journal= {arXiv preprint arXiv:1911.07077},
year = {2019}
}