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

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 `(F)] ^s{\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].