Stochastic Camassa-Holm equation with convection type noise

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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 nd applications to other nonlinear stochastic partial differential equations.
Original languageEnglish
Pages (from-to)404-432
Number of pages29
JournalJournal of Differential Equations
Early online date30 Dec 2020
Publication statusPublished - 5 Mar 2021

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