Global weak solutions for a modified two-component Camassa–Holm equation
Annales de l'I.H.P. Analyse non linéaire, Volume 28 (2011) no. 4, p. 623-641
We obtain the existence of global-in-time weak solutions for the Cauchy problem of a modified two-component Camassa–Holm equation. The global weak solution is obtained as a limit of viscous approximation. The key elements in our analysis are the Helly theorem and some a priori one-sided supernorm and space–time higher integrability estimates on the first-order derivatives of approximation solutions.
Nous obtenons lʼexistence globale en temps de solutions faibles pour le problème de Cauchy dʼune équation modifiée Camassa–Holm à deux composantes. La solution faible globale est obtenue comme une limite de par approximation visqueuse. Les éléments clé dans notre analyse sont le théorème de Helly et certaines estimations a priori de supernorme dʼun seul côté et dʼintégrabilité dans lʼespace-temps des dérivées premières des solutions approchées.
DOI : https://doi.org/10.1016/j.anihpc.2011.04.003
Classification:  35G25,  35L05
Keywords: A modified two-component Camassa–Holm equation, Well-posedness, Blow-up scenario, Strong solution, Global weak solution
@article{AIHPC_2011__28_4_623_0,
     author = {Guan, Chunxia and Yin, Zhaoyang},
     title = {Global weak solutions for a modified two-component Camassa--Holm equation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {28},
     number = {4},
     year = {2011},
     pages = {623-641},
     doi = {10.1016/j.anihpc.2011.04.003},
     zbl = {1241.35159},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2011__28_4_623_0}
}
Guan, Chunxia; Yin, Zhaoyang. Global weak solutions for a modified two-component Camassa–Holm equation. Annales de l'I.H.P. Analyse non linéaire, Volume 28 (2011) no. 4, pp. 623-641. doi : 10.1016/j.anihpc.2011.04.003. http://www.numdam.org/item/AIHPC_2011__28_4_623_0/

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