| 概要 | First, we prove the local well-posedness for the Cauchy problem
of Korteweg-de Vries equation in a quasi 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. Next, we prove an ill-posedness result in the
sense that the flow map (if it exists) is not C2, which is related to
the Diophantine problem. We also prove the global well-posedness in an
almost periodic function space. |