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
收藏
页码：267 / 278
页数：12
相关论文
共 47 条
[1]  
Beals R., 2001, APPL ANAL, V34, P255, DOI [10.1080/00036810108840938, DOI 10.1080/00036810108840938]
[2]   Ostrovsky and Hunter's generic wave equation for weakly dispersive waves: matched asymptotic and pseudospectral study of the paraboloidal travelling waves (corner and near-corner waves) [J].
Boyd, JP .
EUROPEAN JOURNAL OF APPLIED MATHEMATICS, 2005, 16 :65-81
[3]   Microbreaking and polycnoidal waves in the Ostrovsky-Hunter equation [J].
Boyd, JP .
PHYSICS LETTERS A, 2005, 338 (01) :36-43
[4]   Global solutions of the Hunter-Saxton equation [J].
Bressan, A ;
Constantin, A .
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2005, 37 (03) :996-1026
[5]   Global dissipative solutions of the Camassa-Holm equation [J].
Bressan, Alberto ;
Constantin, Adrian .
ANALYSIS AND APPLICATIONS, 2007, 5 (01) :1-27
[6]   Global conservative solutions of the Camassa-Holm equation [J].
Bressan, Alberto ;
Constantin, Adrian .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2007, 183 (02) :215-239
[7]  
Constantin A, 2000, COMMUN PUR APPL MATH, V53, P603
[8]  
Constantin A, 1998, COMMUN PUR APPL MATH, V51, P475, DOI 10.1002/(SICI)1097-0312(199805)51:5<475::AID-CPA2>3.0.CO
[9]  
2-5
[10]   Wave breaking for nonlinear nonlocal shallow water equations [J].
Constantin, A ;
Escher, J .
ACTA MATHEMATICA, 1998, 181 (02) :229-243
12345