2019/11/16 by Sergio Albeverio, Zdzisław Brzeźniak, Albeverio, Sergio +3 · 3 citations
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Fractional Differential Equations Solutions #Geometry and complex manifolds
paper · doi:10.1016/j.jde.2020.12.013
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.