Local wellposedness of the KdV equation with almost periodic initial data
Local wellposedness of the KdV equation with almost periodic initial data

Kotaro Tsugawa, Nagoya University/University of Toronto
Fine Hall 314
We prove the local wellposedness for the Cauchy problem of Kortewegde Vries equation in an almost periodic function space. The function space contains functions satisfying $f=f_1+f_2+...+f_N$ where $f_j$ is in the Sobolev space of order $s>?1/2N$ of $a_j$ periodic functions. Note that f is not periodic when the ratio of periods $a_i/a_j$ is irrational. The main tool of the proof is the Fourier restriction norm method introduced by Bourgain. We also prove an illposedness result in the sense that the flow map (if it exists) is not C2, which is related to the Diophantine problem.