Well-Posedness and Time Regularity for a System of Modified Korteweg-de Vries-Type Equations in Analytic Gevrey Spaces

被引：10

作者：

Boukarou, Aissa ^{[1
]}

Guerbati, Kaddour ^{[1
]}

Zennir, Khaled ^{[2
]}

Alodhaibi, Sultan ^{[2
]}

Alkhalaf, Salem ^{[3
]}

机构：

[1] Univ Ghardaia, Lab Math & Sci Appl, Ghardaia 47000, Algeria

[2] Qassim Univ, Coll Sci & Arts, Dept Math, Ar Rass 51921, Saudi Arabia

[3] Qassim Univ, Coll Sci & Arts, Comp Dept, Ar Rass 51921, Saudi Arabia

来源：

MATHEMATICS | 2020年 / 8卷 / 05期

关键词：

modified Korteweg-de Vries equations; well-posedness; analytic Gevrey spaces; Bourgain spaces; trilinear estimates; time regularity; KDV; DEVRIES; MKDV;

D O I：

10.3390/math8050809

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Studies of modified Korteweg-de Vries-type equations are of considerable mathematical interest due to the importance of their applications in various branches of mechanics and physics. In this article, using trilinear estimate in Bourgain spaces, we show the local well-posedness of the initial value problem associated with a coupled system consisting of modified Korteweg-de Vries equations for given data. Furthermore, we prove that the unique solution belongs to Gevrey space G(sigma) x G(sigma) in x and G(3 sigma) x G(3 sigma) in t. This article is a continuation of recent studies reflected.

引用

页数：16

共 50 条

[31] Well-posedness of stochastic Korteweg-de Vries-Benjamin-Ono equation
Wang, Guolian
Guo, Boling
FRONTIERS OF MATHEMATICS IN CHINA, 2010, 5 (01) : 161 - 177
[32] WELL-POSEDNESS OF KORTEWEG-DE VRIES-BURGERS EQUATION ON A FINITE DOMAIN
Li, Jie
Liu, Kangsheng
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2017, 48 (01): : 91 - 116
[33] Well-posedness of stochastic Korteweg-de Vries-Benjamin-Ono equation
Guolian Wang
Boling Guo
Frontiers of Mathematics in China, 2010, 5 : 161 - 177
[34] Well-posedness of Korteweg-de Vries-Burgers equation on a finite domain
Jie Li
Kangsheng Liu
Indian Journal of Pure and Applied Mathematics, 2017, 48 : 91 - 116
[35] Blowup of solutions of a Korteweg-de Vries-type equation
Yushkov, E. V.
THEORETICAL AND MATHEMATICAL PHYSICS, 2012, 172 (01) : 932 - 938
[36] The radius of convergence and the well-posedness of the Painleve expansions of the Korteweg-de Vries equation
Joshi, N
Srinivasan, GK
NONLINEARITY, 1997, 10 (01) : 71 - 79
[37] Existence for Korteweg-de Vries-type equation with delay
Zhihong Zhao
Erhua Rong
Xiangkui Zhao
Advances in Difference Equations, 2012
[38] Existence for Korteweg-de Vries-type equation with delay
Zhao, Zhihong
Rong, Erhua
Zhao, Xiangkui
ADVANCES IN DIFFERENCE EQUATIONS, 2012,
[39] Local well-posedness and time regularity for a fifth-order shallow water equations in analytic Gevrey–Bourgain spaces
Aissa Boukarou
Kaddour Guerbati
Khaled Zennir
Monatshefte für Mathematik, 2020, 193 : 763 - 782
[40] Integrable symplectic maps associated with discrete Korteweg-de Vries-type equations
Xu, Xiaoxue
Jiang, Mengmeng
Nijhoff, Frank W.
STUDIES IN APPLIED MATHEMATICS, 2021, 146 (01) : 233 - 278

← 1 2 3 4 5 →