Well-posedness of stochastic modified Kawahara equation

被引：26

作者：

Agarwal, P. ^{[1
,2
,3
,4
]}

Hyder, Abd-Allah ^{[5
,6
]}

Zakarya, M. ^{[5
,7
]}

机构：

[1] Anand Int Coll Engn, Dept Math, Jaipur, Rajasthan, India

[2] Netaji Subhas Univ Technol, Dept Math, New Delhi, India

[3] Harish Chandra Res Inst HRI, Dept Math, Allahbad, India

[4] Int Ctr Basic & Appl Sci, Jaipur, Rajasthan, India

[5] King Khalid Univ, Dept Math, Coll Sci, Abha, Saudi Arabia

[6] Al Azhar Univ, Dept Engn Math & Phys, Fac Engn, Cairo, Egypt

[7] Al Azhar Univ, Dept Math, Fac Sci, Assiut, Egypt

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2020年 / 2020卷 / 01期

关键词：

Modified Kawahara equation; Well-posedness; Wiener process; Fixed point theorem; Fourier restriction method; WATER-WAVES; EXISTENCE; MODEL;

D O I：

10.1186/s13662-019-2485-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页数：10

共 25 条

[1] ON THE EXCITATION OF LONG NONLINEAR WATER-WAVES BY A MOVING PRESSURE DISTRIBUTION [J].