JournalsaihpcVol. 32, No. 2pp. 443–469

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

  • Wei Yan

    College of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan 453007, PR China

  • Yongsheng Li

    Department of Mathematics, South China University of Technology, Guangzhou, Guangdong 510640, PR China
The Cauchy problem for the modified two-component Camassa–Holm system in critical Besov space cover
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Abstract

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.

Cite this article

Wei Yan, Yongsheng Li, The Cauchy problem for the modified two-component Camassa–Holm system in critical Besov space. Ann. Inst. H. Poincaré Anal. Non Linéaire 32 (2015), no. 2, pp. 443–469

DOI 10.1016/J.ANIHPC.2014.01.003