THE GLOBAL ATTRACTOR FOR A VISCOUS WEAKLY DISSIPATIVE GENERALIZED TWO-COMPONENT μ-HUNTER-SAXTON SYSTEM

doi:10.1016/S0252-9602(18)30772-0

数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (2): 651-672.doi: 10.1016/S0252-9602(18)30772-0

THE GLOBAL ATTRACTOR FOR A VISCOUS WEAKLY DISSIPATIVE GENERALIZED TWO-COMPONENT μ-HUNTER-SAXTON SYSTEM

张磊, 刘斌

School of Mathematics and Statistics, Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan 430074, China

收稿日期:2016-11-09 修回日期:2017-05-17 出版日期:2018-04-25 发布日期:2018-04-25
通讯作者: Bin LIU E-mail:binliu@mail.hust.edu.cn
作者简介:Lei ZHANG,E-mail:lzhang890701@163.com
基金资助:
This work was partially supported by NNSF of China (11571126, 11701198), and China Postdoctoral Science Foundation funded project (2017M622397).

THE GLOBAL ATTRACTOR FOR A VISCOUS WEAKLY DISSIPATIVE GENERALIZED TWO-COMPONENT μ-HUNTER-SAXTON SYSTEM

Lei ZHANG, Bin LIU

School of Mathematics and Statistics, Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan 430074, China

Received:2016-11-09 Revised:2017-05-17 Online:2018-04-25 Published:2018-04-25
Contact: Bin LIU E-mail:binliu@mail.hust.edu.cn
Supported by:
This work was partially supported by NNSF of China (11571126, 11701198), and China Postdoctoral Science Foundation funded project (2017M622397).

摘要/Abstract

摘要：

This article is concerned with the existence of global attractor of a weakly dissipative generalized two-component μ-Hunter-Saxton (gμHS2) system with viscous terms. Under the period boundary conditions and with the help of the Galerkin procedure and compactness method, we first investigate the existence of global solution for the viscous weakly dissipative (gμHS2) system. On the basis of some uniformly prior estimates of the solution to the viscous weakly dissipative (gμHS2) system, we show that the semi-group of the solution operator {S(t)}_t ≥ 0 has a bounded absorbing set. Moreover, we prove that the dynamical system {S(t)}_t ≥ 0 possesses a global attractor in the Sobolev space H²(S)×H²(S).

关键词: Generalized two-component μ-Hunter-Saxton system, viscous weakly dissipative, existence, global attractor, period boundary conditions

Abstract:

Key words: Generalized two-component μ-Hunter-Saxton system, viscous weakly dissipative, existence, global attractor, period boundary conditions

张磊, 刘斌. THE GLOBAL ATTRACTOR FOR A VISCOUS WEAKLY DISSIPATIVE GENERALIZED TWO-COMPONENT μ-HUNTER-SAXTON SYSTEM[J]. 数学物理学报(英文版), 2018, 38(2): 651-672.

Lei ZHANG, Bin LIU. THE GLOBAL ATTRACTOR FOR A VISCOUS WEAKLY DISSIPATIVE GENERALIZED TWO-COMPONENT μ-HUNTER-SAXTON SYSTEM[J]. Acta mathematica scientia,Series B, 2018, 38(2): 651-672.

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THE GLOBAL ATTRACTOR FOR A VISCOUS WEAKLY DISSIPATIVE GENERALIZED TWO-COMPONENT μ-HUNTER-SAXTON SYSTEM

THE GLOBAL ATTRACTOR FOR A VISCOUS WEAKLY DISSIPATIVE GENERALIZED TWO-COMPONENT μ-HUNTER-SAXTON SYSTEM

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