Well-posedness of stochastic modified Kawahara equation

P. Agarwal; Abd Allah Hyder; M. Zakarya

doi:10.1186/s13662-019-2485-6

Well-posedness of stochastic modified Kawahara equation

P. Agarwal
, Abd Allah Hyder
, M. Zakarya

International College of Engineering
Netaji Subhas University of Technology
Harish Chandra Research Institute
International Center for Basic and Applied Sciences
King Khalid University
Al-Azhar University

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

32 Scopus citations

Abstract

In this paper we consider the Cauchy problem for the stochastic modified Kawahara equation, which is a fifth-order shallow water wave equation. We prove local well-posedness for data in H^s(R) , s≥ − 1 / 4. Moreover, we get the global existence for L²(R) solutions. Due to the non-zero singularity of the phase function, a fixed point argument and the Fourier restriction method are proposed.

Original language	English
Article number	18
Journal	Advances in Difference Equations
Volume	2020
Issue number	1
DOIs	https://doi.org/10.1186/s13662-019-2485-6
State	Published - 1 Dec 2020
Externally published	Yes

Keywords

Fixed point theorem
Fourier restriction method
Modified Kawahara equation
Well-posedness
Wiener process

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10.1186/s13662-019-2485-6

Cite this

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title = "Well-posedness of stochastic modified Kawahara equation",

abstract = "In this paper we consider the Cauchy problem for the stochastic modified Kawahara equation, which is a fifth-order shallow water wave equation. We prove local well-posedness for data in Hs(R) , s≥ − 1 / 4. Moreover, we get the global existence for L2(R) solutions. Due to the non-zero singularity of the phase function, a fixed point argument and the Fourier restriction method are proposed.",

keywords = "Fixed point theorem, Fourier restriction method, Modified Kawahara equation, Well-posedness, Wiener process",

author = "P. Agarwal and Hyder, \{Abd Allah\} and M. Zakarya",

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AU - Hyder, Abd Allah

AU - Zakarya, M.

PY - 2020/12/1

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N2 - In this paper we consider the Cauchy problem for the stochastic modified Kawahara equation, which is a fifth-order shallow water wave equation. We prove local well-posedness for data in Hs(R) , s≥ − 1 / 4. Moreover, we get the global existence for L2(R) solutions. Due to the non-zero singularity of the phase function, a fixed point argument and the Fourier restriction method are proposed.

AB - In this paper we consider the Cauchy problem for the stochastic modified Kawahara equation, which is a fifth-order shallow water wave equation. We prove local well-posedness for data in Hs(R) , s≥ − 1 / 4. Moreover, we get the global existence for L2(R) solutions. Due to the non-zero singularity of the phase function, a fixed point argument and the Fourier restriction method are proposed.

KW - Fixed point theorem

KW - Fourier restriction method

KW - Modified Kawahara equation

KW - Well-posedness

KW - Wiener process

UR - https://www.scopus.com/pages/publications/85077560834

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DO - 10.1186/s13662-019-2485-6

M3 - Article

AN - SCOPUS:85077560834

SN - 1687-1839

VL - 2020

JO - Advances in Difference Equations

JF - Advances in Difference Equations

IS - 1

M1 - 18

ER -

Well-posedness of stochastic modified Kawahara equation

Abstract

Keywords

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