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

Guan, Chunxia; Yin, Zhaoyang

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

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.

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.

Classification : 35G25, 35L05
Mots clés : A modified two-component Camassa–Holm equation, Well-posedness, Blow-up scenario, Strong solution, Global weak solution

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