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Well-posedness and analytic solutions of the two-component Euler–Poincaré system

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Abstract

We first establish the local well-posedness for the Cauchy problem of the two-component Euler–Poincaré system in nonhomogeneous Besov spaces. Then, we derive a blow-up criterion for strong solutions to the system. Finally, we prove the existence of analytic solutions to the system.

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Acknowledgments

This work was partially supported by NNSFC (No. 11271382), RFDP (No. 20120171110014), FDCT (No. 098/2013/A3), Guangdong Special Support Program (No. 8-2015), and the key project of NSF of Guangdong province (No. 2016A030311004). The authors thank the referee for valuable comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, China

    Jinlu Li & Zhaoyang Yin

  2. Faculty of Information Technology, Macau University of Science and Technology, Macau, China

    Zhaoyang Yin

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  1. Jinlu Li
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  2. Zhaoyang Yin
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Correspondence to Jinlu Li.

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Communicated by A. Constantin.

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Li, J., Yin, Z. Well-posedness and analytic solutions of the two-component Euler–Poincaré system. Monatsh Math 183, 509–537 (2017). https://doi.org/10.1007/s00605-016-0927-8

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  • DOI: https://doi.org/10.1007/s00605-016-0927-8

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