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Stochastic Camassa-Holm equation with convection type noise

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JournalJournal of Differential Equations
DateAccepted/In press - 10 Dec 2020
DateE-pub ahead of print (current) - 30 Dec 2020
DatePublished - 5 Mar 2021
Volume276
Number of pages29
Pages (from-to)404-432
Early online date30/12/20
Original languageEnglish

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 nd applications to other nonlinear stochastic partial differential equations.

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© 2020 Published by Elsevier Inc.This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy.

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