Wave Seminar: Global well-posedness for the Kawahara equation with low regularity data

2011-12-6 14:45 - 2011-12-6 16:15
Faculty of Science Building #3 Room 205
Takamori Kato (Kyoto University)
In this talk, we consider the well-posedness for the Cauchy problem of the Kawahara equation which is one of fifth order KdV type equations. Firstly, we establish the local well-posedness for $s \geq -2$ by a variant of the Fourier restriction norm method. This result is optimal in some sense.

Secondly, we extend the local-in-time solutions to the global ones by the I-method. Note that it is difficult to apply the I-method to the modified Bourgain space. Then we establish the sharp bilinear refinement to overcome this difficulty. The main topic of this talk is the proof of the almost conservation laws for the modified Bourgain space, which is the key estimate in the I-method.