Geodesic
Initial data problems for the two-component Camassa-Holm system
Electronic journal of differential equations, Tome 2014 (2014)
This article concerns the study of some properties of the two-component Camassa-Holm system. By constructing two sequences of solutions of the two-component Camassa-Holm system, we prove that the solution map of the Cauchy problem of the two-component Camassa-Holm system is not uniformly continuous in $H^s(\mathbb{R}), s>5/2$.
Classification : 35G25, 35B30, 35L05
Keywords: non-uniform dependence, Camassa-Holm system, well-posedness, energy estimates, initial value problem 
@article{EJDE_2014__2014__a140,
     author = {Wang,  Xiaohuan},
     title = {Initial data problems for the two-component {Camassa-Holm} system},
     journal = {Electronic journal of differential equations},
     year = {2014},
     volume = {2014},
     zbl = {1297.35086},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a140/}
}
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JO  - Electronic journal of differential equations
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%A Wang,  Xiaohuan
%T Initial data problems for the two-component Camassa-Holm system
%J Electronic journal of differential equations
%D 2014
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%U http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a140/
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%F EJDE_2014__2014__a140
Wang,  Xiaohuan. Initial data problems for the two-component Camassa-Holm system. Electronic journal of differential equations, Tome 2014 (2014). http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a140/