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382877

The well-posedness of stochastic Kawahara equation: fixed point argument and Fourier restriction method

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Last updated: 05 Jan 2025

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Abstract

In this paper, we investigate the Cauchy problem for the stochastic Kawahara equation,
which is a fifth-order shallow water wave equation. We prove local well-posedness for
data in Hs (R), s > −7/4. Moreover, we get global existence for L2(R) solutions. Due to
the non-zero singularity of the phase function, a fixed point argument and Fourier
restriction method are proposed.

DOI

10.1186/s42787-019-0006-0

Keywords

Kawahara equation, well-posedness, Wiener process, Fixed point theorem, Fourier restriction method

Authors

First Name

Abd-Allah

Last Name

Hyder

MiddleName

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Affiliation

Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004 Abha, Saudi Arabia

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Orcid

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First Name

M.

Last Name

Zakarya

MiddleName

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Affiliation

Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004 Abha, Saudi Arabia

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Volume

27

Article Issue

1

Related Issue

50652

Issue Date

2019-12-01

Receive Date

2024-09-30

Publish Date

2019-12-01

Page Start

1

Page End

10

Print ISSN

1110-256X

Online ISSN

2090-9128

Article File

JOEMS_Volume 27_Issue 1_Pages 1-10.pdf

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https://joems.journals.ekb.eg/article_382877.html

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https://joems.journals.ekb.eg/service?article_code=382877

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Publication Title

Journal of the Egyptian Mathematical Society

Publication Link

https://joems.journals.ekb.eg/

MainTitle

The well-posedness of stochastic Kawahara equation: fixed point argument and Fourier restriction method

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Article

Created At

21 Dec 2024