The Cauchy problem for the modified two-component Camassa–Holm system in critical Besov space

Yan, Wei; Li, Yongsheng

doi:10.1016/j.anihpc.2014.01.003

Yan, Wei ; Li, Yongsheng

Annales de l'I.H.P. Analyse non linéaire, Tome 32 (2015) no. 2, pp. 443-469.

Résumé

In this paper, we are concerned with the Cauchy problem for the modified two-component Camassa–Holm system in the Besov space with data having critical regularity. The key elements in our paper are the real interpolations and logarithmic interpolation among inhomogeneous Besov space and Lemma 5.2.1 of [7] which is also called Osgood Lemma and the Fatou Lemma. The new ingredient that we introduce in this paper can be seen on pages 453–457.

MR Zbl

DOI : 10.1016/j.anihpc.2014.01.003

Classification : 35G25, 35L05, 35R25
Mots-clés : Cauchy problem, Modified two-component Camassa–Holm system, Critical Besov space, Osgood Lemma

@article{AIHPC_2015__32_2_443_0,
     author = {Yan, Wei and Li, Yongsheng},
     title = {The {Cauchy} problem for the modified two-component {Camassa{\textendash}Holm} system in critical {Besov} space},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {443--469},
     publisher = {Elsevier},
     volume = {32},
     number = {2},
     year = {2015},
     doi = {10.1016/j.anihpc.2014.01.003},
     mrnumber = {3325245},
     zbl = {1336.35121},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2014.01.003/}
}

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Yan, Wei; Li, Yongsheng. The Cauchy problem for the modified two-component Camassa–Holm system in critical Besov space. Annales de l'I.H.P. Analyse non linéaire, Tome 32 (2015) no. 2, pp. 443-469. doi : 10.1016/j.anihpc.2014.01.003. http://www.numdam.org/articles/10.1016/j.anihpc.2014.01.003/

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