Global well-posedness of periodic KP-I initial value problem in the energy space
arXiv:1202.5801
Abstract
The periodic KP-I initial value problem $\partial_t u+\partial_x^3 u-\partial_x^{-1}\partial_y^2 u+\partial_x (u^2/2)=0$ on $T_{x,y}^2\times R_t, $u(0)=Ï$ is globally well-posed in the energy space $E^1 = E^1 (T^2)=Ï: T^2\to R:\hatÏ(0,n)=0$ for all $n\in Z \ 0$ and $||Ï||_{E^1 (T^2)}=||\hatÏ(m,n)(1+|m|+|n/m|)||_{l^2(Z^2)}<\infty$.
This paper has been withdrawn by the author due to an error in the orthogonality proof