Wave Seminar: Global wellposedness for the Kawahara equation with low regularity data
 Date

2011126 14:45 
2011126 16:15
 Place
 Faculty of Science Building #3 Room 205

Speaker/Organizer
 Takamori Kato (Kyoto University)

 In this talk, we consider the wellposedness for the Cauchy problem of the Kawahara equation which is one of fifth order KdV type equations. Firstly, we establish the local wellposedness for $s \geq 2$ by a variant of the Fourier restriction norm method. This result is optimal in some sense.
Secondly, we extend the localintime solutions to the global ones by the Imethod. Note that it is difficult to apply the Imethod 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 Imethod.