Solvability of the Stochastic Degasperis-Procesi Equation

Lynnyngs K. Arruda; Nikolai V. Chemetov; Fernanda Cipriano

doi:10.1007/s10884-021-10021-5

Solvability of the Stochastic Degasperis-Procesi Equation

Lynnyngs K. Arruda, Nikolai V. Chemetov, Fernanda Cipriano

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

1 Citation (Scopus)

Abstract

This article studies the Stochastic Degasperis-Procesi equation on R with an additive noise. Applying the kinetic theory, and considering the initial conditions in L²(R) ∩ L²⁺^δ(R) , for arbitrary small δ> 0 , we establish the existence of a global pathwise solution. Restricting to the particular case of zero noise, our result improves the deterministic solvability results that exist in the literature.

Original language	English
Journal	Journal of Dynamics and Differential Equations
DOIs	https://doi.org/10.1007/s10884-021-10021-5
Publication status	Accepted/In press - 2021

Keywords

Degasperis-Procesi equation
Solvability
Stochastic

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10.1007/s10884-021-10021-5

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@article{d6fff221cd4740c58a85693cc39df38f,

title = "Solvability of the Stochastic Degasperis-Procesi Equation",

abstract = "This article studies the Stochastic Degasperis-Procesi equation on R with an additive noise. Applying the kinetic theory, and considering the initial conditions in L2(R) ∩ L2+δ(R) , for arbitrary small δ> 0 , we establish the existence of a global pathwise solution. Restricting to the particular case of zero noise, our result improves the deterministic solvability results that exist in the literature.",

keywords = "Degasperis-Procesi equation, Solvability, Stochastic",

author = "Arruda, {Lynnyngs K.} and Chemetov, {Nikolai V.} and Fernanda Cipriano",

note = "info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UID%2FMAT%2F00297%2F2019/PT# Funding Information: Lynnyngs K. Arruda acknowledges support from FAPESP (Funda{\c c}{\~a}o de Amparo {\`a} Pesquisa do Estado de S{\~a}o Paulo - Brazil), Grant 2017/23751-2. ",

year = "2021",

doi = "10.1007/s10884-021-10021-5",

language = "English",

journal = "Journal of Dynamics and Differential Equations",

issn = "1040-7294",

publisher = "Springer New York",

}

TY - JOUR

T1 - Solvability of the Stochastic Degasperis-Procesi Equation

AU - Arruda, Lynnyngs K.

AU - Chemetov, Nikolai V.

AU - Cipriano, Fernanda

N1 - info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UID%2FMAT%2F00297%2F2019/PT# Funding Information: Lynnyngs K. Arruda acknowledges support from FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo - Brazil), Grant 2017/23751-2.

PY - 2021

Y1 - 2021

N2 - This article studies the Stochastic Degasperis-Procesi equation on R with an additive noise. Applying the kinetic theory, and considering the initial conditions in L2(R) ∩ L2+δ(R) , for arbitrary small δ> 0 , we establish the existence of a global pathwise solution. Restricting to the particular case of zero noise, our result improves the deterministic solvability results that exist in the literature.

AB - This article studies the Stochastic Degasperis-Procesi equation on R with an additive noise. Applying the kinetic theory, and considering the initial conditions in L2(R) ∩ L2+δ(R) , for arbitrary small δ> 0 , we establish the existence of a global pathwise solution. Restricting to the particular case of zero noise, our result improves the deterministic solvability results that exist in the literature.

KW - Degasperis-Procesi equation

KW - Solvability

KW - Stochastic

UR - http://www.scopus.com/inward/record.url?scp=85108152935&partnerID=8YFLogxK

U2 - 10.1007/s10884-021-10021-5

DO - 10.1007/s10884-021-10021-5

M3 - Article

AN - SCOPUS:85108152935

JO - Journal of Dynamics and Differential Equations

JF - Journal of Dynamics and Differential Equations

SN - 1040-7294

ER -

Solvability of the Stochastic Degasperis-Procesi Equation

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Keywords

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