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Globalwell-posedness and I method for the fifth order Korteweg-de Vries equation

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Abstract

The Kawahara equation has fewer symmetries than the KdV equation; in particular, it has no invariant scaling transform and is not completely integrable. Thus its analysis requires different methods. We prove that the Kawahara equation is locally well posed in H −7/4, using the ideas of an \({\overline F ^s}\)-type space [8]. Then we show that the equation is globally well posed in H s for s ≥ −7/4, using the ideas of the “I-method” [7].

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Authors and Affiliations

  1. Institute of Applied Physics and Computational Mathematics, P. O. Box 8009, Beijing, 100088, China

    Wengu Chen

  2. LMAM, School of Mathematical Sciences, Peking University, Beijing, 100871, China

    Zihua Guo

Authors
  1. Wengu Chen
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  2. Zihua Guo
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Correspondence to Wengu Chen.

Additional information

supported in part by the NNSF of China (Nos. 10771130, 10931001).

supported in part by NNSF of China (NO. 11001003).

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Chen, W., Guo, Z. Globalwell-posedness and I method for the fifth order Korteweg-de Vries equation. JAMA 114, 121–156 (2011). https://doi.org/10.1007/s11854-011-0014-y

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  • DOI: https://doi.org/10.1007/s11854-011-0014-y

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