scholarly journals Global weak solutions for the two-component Novikov equation

2020 ◽  
Vol 28 (4) ◽  
pp. 1545-1562
Author(s):  
Cheng He ◽  
◽  
Changzheng Qu
Keyword(s):  
Weak Solutions ◽  
Global Weak Solutions ◽  
Two Component ◽  
Novikov Equation

On the existence of global weak solutions to an integrable two-component Camassa–Holm shallow-water system

2013 ◽  
Vol 56 (3) ◽  
pp. 755-775 ◽  
Author(s):  
Chunxia Guan ◽  
Zhaoyang Yin
Keyword(s):  
Shallow Water ◽  
Weak Solutions ◽  
Burgers Equation ◽  
Water System ◽  
Global Weak Solution ◽  
Rarefaction Waves ◽  
Global Weak Solutions ◽  
Two Component ◽  
The Cauchy Problem ◽  
Shallow Water System

AbstractIn this paper, we investigate the existence of global weak solutions to an integrable two-component Camassa–Holm shallow-water system, provided the initial datau0(x)andρ0(x)have end statesu± andρ±, respectively. By perturbing the Cauchy problem of the system around rarefaction waves of the well-known Burgers equation, we obtain a global weak solution for the system under the assumptionsu− ≤ u+andρ− ≤ ρ+.

scholarly journals Lipschitz metric for the modified two-component Camassa–Holm system

2018 ◽  
Vol 16 (02) ◽  
pp. 159-182 ◽  
Author(s):  
Chunxia Guan ◽  
Kai Yan ◽  
Xuemei Wei
Keyword(s):  
Energy Density ◽  
Real Line ◽  
Weak Solutions ◽  
Lipschitz Continuity ◽  
Distance Functions ◽  
Lagrangian Coordinates ◽  
Global Weak Solutions ◽  
Positive Radon Measure ◽  
Two Component ◽  
Lipschitz Metric

This paper is devoted to the existence and Lipschitz continuity of global conservative weak solutions in time for the modified two-component Camassa–Holm system on the real line. We obtain the global weak solutions via a coordinate transformation into the Lagrangian coordinates. The key ingredients in our analysis are the energy density given by the positive Radon measure and the proposed new distance functions as well.

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