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.

Self-similar solutions and blow-up phenomena for a two-component shallow water system

2013 ◽  
Vol 33 (3) ◽  
pp. 821-829
Author(s):  
Shouming ZHOU ◽  
Chunlai MU ◽  
Liangchen WANG
Keyword(s):  
Shallow Water ◽  
Blow Up ◽  
Water System ◽  
Two Component ◽  
Shallow Water System ◽  
Self Similar ◽  
Similar Solutions

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.

scholarly journals Numerical model of shallow water dynamics in the channel of the Volga: estimation of roughness

2013 ◽  
pp. 114-130 ◽  
Author(s):  
A.V. Pisarev ◽  
◽  
S.S. Khrapov ◽  
E.O. Agafonnikova ◽  
A.V. Khoperskov ◽  
...  
Keyword(s):  
Numerical Model ◽  
Shallow Water ◽  
Water Dynamics ◽  
Shallow Water Dynamics

Solitary Waves, Shock Waves and Singular Solitons of Gardner's Equation for Shallow Water Dynamics

2014 ◽  
Vol 45 (6) ◽  
pp. 1135
Author(s):  
A.K. Daoui ◽  
H. Triki ◽  
M. Mirzazadeh ◽  
A. Biswas
Keyword(s):  
Shock Waves ◽  
Shallow Water ◽  
Solitary Waves ◽  
Water Dynamics ◽  
Shallow Water Dynamics

A “vortex in cell” model for quasi-geostrophic, shallow water dynamics on the sphere

2010 ◽  
Vol 32 (3-4) ◽  
pp. 132-142 ◽  
Author(s):  
A. Mohammadian ◽  
John Marshall
Keyword(s):  
Shallow Water ◽  
Cell Model ◽  
Water Dynamics ◽  
Shallow Water Dynamics

Wave breaking and shock waves for a periodic shallow water equation

2007 ◽  
Vol 365 (1858) ◽  
pp. 2281-2289 ◽  
Author(s):  
Joachim Escher
Keyword(s):  
Shock Waves ◽  
Shallow Water ◽  
Wave Breaking ◽  
Blow Up ◽  
Shallow Water Equation ◽  
Strong Solutions ◽  
Global Weak Solutions ◽  
Initial Profile ◽  
And Shock Waves ◽  
Periodic Shock

This paper is devoted to the study of a recently derived periodic shallow water equation. We discuss in detail the blow-up scenario of strong solutions and present several conditions on the initial profile, which ensure the occurrence of wave breaking. We also present a family of global weak solutions, which may be viewed as global periodic shock waves to the equation under discussion.

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