Global existence for the periodic dispersive Hunter-Saxton equation

被引：0

作者：

Ye, Weikui ^{[1
]}

Yin, Zhaoyang ^{[1
,2
]}

机构：

[1] Sun Yat Sen Univ, Dept Math, Guangzhou 510275, Peoples R China

[2] Macau Univ Sci & Technol, Fac Informat Technol, Taipa, Macao, Peoples R China

来源：

MONATSHEFTE FUR MATHEMATIK | 2020年 / 191卷 / 02期

基金：

中国国家自然科学基金;

关键词：

The periodic dispersive Hunter-Saxton equation; Local well-posedness; The Kato method; Global existence; SHALLOW-WATER EQUATION; CAMASSA-HOLM; WELL-POSEDNESS; WAVE BREAKING; PARTICLE TRAJECTORIES; DISSIPATIVE SOLUTIONS; WEAK SOLUTIONS; SHORT-PULSE; OSTROVSKY; SCATTERING;

D O I：

10.1007/s00605-019-01290-w

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study an integrable dispersive Hunter-Saxton equation in periodic domain. Firstly, we establish the local well-posedness of the Cauchy problem of the equation in Hs(S),s >= 2, by applying the Kato method. Then, based on a sign-preserve property, we obtain a global existence result for the equation. Moreover, we extend the obtained result to some periodic nonlinear partial differential equations of second order of the general form.

引用

页码：267 / 278

页数：12

共 50 条

[41] Long-time asymptotics of the Hunter-Saxton equation on the line [J].

Ju, Luman ;

Xu, Kai ;

Fan, Engui .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2024, 390 :451-493

[42] On initial boundary value problems for variants of the Hunter-Saxton equation [J].

Kohlmann, Martin .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2012, 63 (03) :441-452

[43] GLOBAL ESTIMATES AND BLOW-UP CRITERIA FOR THE GENERALIZED HUNTER-SAXTON SYSTEM [J].

Sarria, Alejandro .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2015, 20 (02) :641-673

[44] ON THE Lp REGULARITY OF SOLUTIONS TO THE GENERALIZED HUNTER-SAXTON SYSTEM [J].

Choi, Jaeho ;

Krishna, Nitin ;

Magill, Nicole ;

Sarria, Alejandro .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2019, 24 (12) :6349-6365

[45] Maximal dissipation in Hunter-Saxton equation for bounded energy initial data [J].

Cieslak, Tomasz ;

Jamroz, Grzegorz .

ADVANCES IN MATHEMATICS, 2016, 290 :590-613

[46] Novel symmetric structures and explicit solutions to a coupled Hunter-Saxton equation [J].

Zhao, Qiulan ;

Wang, Huanjin ;

Li, Xinyue .

PHYSICA SCRIPTA, 2023, 98 (06)

[47] Characteristic boundary layers in the vanishing viscosity limit for the Hunter-Saxton equation [J].

Peng, Lei ;

Li, Jingyu ;

Mei, Ming ;

Zhang, Kaijun .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2024, 386 :164-195

[48] Spheres, Kahler geometry and the Hunter-Saxton system [J].

Lenells, Jonatan .

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2013, 469 (2154)

[49] THE GLOBAL ATTRACTOR FOR A VISCOUS WEAKLY DISSIPATIVE GENERALIZED TWO-COMPONENT μ-HUNTER-SAXTON SYSTEM [J].

Zhang, Lei ;

Liu, Bin .

ACTA MATHEMATICA SCIENTIA, 2018, 38 (02) :651-672

[50] Algebro-geometric solutions for the Hunter-Saxton hierarchy [J].

Hou, Yu ;

Fan, Engui ;

Zhao, Peng .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2014, 65 (03) :487-520

← 1 2 3 4 5 →