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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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