scholarly journals Wave-Breaking Criterion for the Generalized Weakly Dissipative Periodic Two-Component Hunter-Saxton System

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Jianmei Zhang ◽  
Lixin Tian
Keyword(s):  
Wave Breaking ◽  
Well Posedness ◽  
Two Component ◽  
Periodic Setting

This paper studies the wave-breaking criterion for the generalized weakly dissipative two-component Hunter-Saxton system in the periodic setting. We get local well-posedness for the generalized weakly dissipative two-component Hunter-Saxton system. We study a wave-breaking criterion for solutions and results of wave-breaking solutions with certain initial profiles.

scholarly journals Blow-Up Analysis for the Periodic Two-Component μ-Hunter-Saxton System

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Yunxi Guo ◽  
Tingjian Xiong
Keyword(s):  
Transport Equation ◽  
Wave Breaking ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Blow Up Analysis ◽  
Classic Method ◽  
Two Component ◽  
Localization Analysis ◽  
Spatially Periodic ◽  
Periodic Setting

The two-component μ-Hunter-Saxton system is considered in the spatially periodic setting. Firstly, a wave-breaking criterion is derived by employing the localization analysis of the transport equation theory. Secondly, several sufficient conditions of the blow-up solutions are established by using the classic method. The results obtained in this paper are new and different from those in previous works.

On the wave-breaking phenomena for the two-component Dullin-Gottwald-Holm system

2012 ◽  
Vol 86 (3) ◽  
pp. 810-834 ◽  
Author(s):  
Fei Guo ◽  
Hongjun Gao ◽  
Yue Liu
Keyword(s):  
Wave Breaking ◽  
Two Component

scholarly journals On the Blow-Up of Solutions of a Weakly Dissipative Modified Two-Component Periodic Camassa-Holm System

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Yongsheng Mi ◽  
Chunlai Mu ◽  
Weian Tao
Keyword(s):  
Cauchy Problem ◽  
Blow Up ◽  
Strong Solutions ◽  
Well Posedness ◽  
Holm Equation ◽  
Two Component ◽  
The Cauchy Problem ◽  
Blow Up Rate

We study the Cauchy problem of a weakly dissipative modified two-component periodic Camassa-Holm equation. We first establish the local well-posedness result. Then we derive the precise blow-up scenario and the blow-up rate for strong solutions to the system. Finally, we present two blow-up results for strong solutions to the system.

scholarly journals Wave breaking for a generalized weakly dissipative two-component Camassa–Holm system

2013 ◽  
Vol 400 (2) ◽  
pp. 406-417 ◽  
Author(s):  
Wenxia Chen ◽  
Lixin Tian ◽  
Xiaoyan Deng ◽  
Jianmei Zhang
Keyword(s):  
Wave Breaking ◽  
Two Component

Stability of blow-up solution for the two component Camassa–Holm equations

2020 ◽  
Vol 120 (3-4) ◽  
pp. 319-336
Author(s):  
Xintao Li ◽  
Shoujun Huang ◽  
Weiping Yan
Keyword(s):  
Shallow Water ◽  
Wave Breaking ◽  
Water Regime ◽  
Blow Up ◽  
Dynamical Behavior ◽  
Water Dynamics ◽  
Two Component ◽  
Breaking Mechanism ◽  
Self Similar ◽  
Shallow Water Dynamics

This paper studies the wave-breaking mechanism and dynamical behavior of solutions near the explicit self-similar singularity for the two component Camassa–Holm equations, which can be regarded as a model for shallow water dynamics and arising from the approximation of the Hamiltonian for Euler’s equation in the shallow water regime.

Wave breaking analysis for the periodic rotation-two-component Camassa–Holm system

2019 ◽  
Vol 187 ◽  
pp. 214-228
Author(s):  
Jingjing Liu ◽  
Patrizia Pucci ◽  
Qihu Zhang
Keyword(s):  
Wave Breaking ◽  
Periodic Rotation ◽  
Two Component
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