Global weak solutions for a modified two-component Camassa–Holm equation

Guan, Chunxia; Yin, Zhaoyang

doi:10.1016/j.anihpc.2011.04.003

Guan, Chunxia ; Yin, Zhaoyang

Annales de l'I.H.P. Analyse non linéaire, Tome 28 (2011) no. 4, pp. 623-641

Abstract (VO)
Résumé

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.

Zbl | 1 citation dans Numdam

DOI : 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

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     author = {Guan, Chunxia and Yin, Zhaoyang},
     title = {Global weak solutions for a modified two-component {Camassa{\textendash}Holm} equation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {623--641},
     year = {2011},
     publisher = {Elsevier},
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     doi = {10.1016/j.anihpc.2011.04.003},
     zbl = {1241.35159},
     language = {en},
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}

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Guan, Chunxia; Yin, Zhaoyang. Global weak solutions for a modified two-component Camassa–Holm equation. Annales de l'I.H.P. Analyse non linéaire, Tome 28 (2011) no. 4, pp. 623-641. doi: 10.1016/j.anihpc.2011.04.003

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