Stochastic Camassa-Holm equation with convection type noise

Sergio Albeverio; Zdzislaw Brzezniak; Alex Daletskii

doi:10.1016/j.jde.2020.12.013

Stochastic Camassa-Holm equation with convection type noise

Sergio Albeverio, Zdzislaw Brzezniak, Alex Daletskii

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	404-432
Number of pages	29
Journal	Journal of Differential Equations
Volume	276
Early online date	30 Dec 2020
DOIs	https://doi.org/10.1016/j.jde.2020.12.013
Publication status	Published - 5 Mar 2021

Bibliographical note

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10.1016/j.jde.2020.12.013

Daletskii & Brzezniak_Camassa-Holm-Kato_2d_Revision_Aug_30-final_AAM
© 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.
Accepted author manuscript, 360 KBLicence: CC BY-NC-ND

Cite this

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title = "Stochastic Camassa-Holm equation with convection type noise",

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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AU - Albeverio, Sergio

AU - Brzezniak, Zdzislaw

AU - Daletskii, Alex

PY - 2021/3/5

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N2 - 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.

AB - 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.

U2 - 10.1016/j.jde.2020.12.013

DO - 10.1016/j.jde.2020.12.013

M3 - Article

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JO - Journal of Differential Equations

JF - Journal of Differential Equations

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