Journal d'Analyse Mathématique

, 114:121 | Cite as

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].

Keywords

Cauchy Problem Bilinear Estimate Nonlinear Dispersive Equation Invariant Scaling Kawahara Equation 
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Copyright information

© Hebrew University Magnes Press 2011

Authors and Affiliations

  1. 1.Institute of Applied Physics and Computational MathematicsBeijingChina
  2. 2.LMAM, School of Mathematical SciencesPeking UniversityBeijingChina

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