Global well-posedness of periodic KP-I initial value problem in the energy space

Details Global well-posedness of periodic KP-I initial value problem in the energy space Global well-posedness of periodic KP-I initial value problem in the energy space

2012-02-26

arxiv.org/abs/1202.5801v2

Mathematics

Analysis of PDEs

This paper has been withdrawn by the author due to an error in the orthogonality proof

Scientific paper

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,
$u(0)=\phi$ is globally well-posed in the energy space $E^1 = E^1 (T^2)=\phi:
T^2\to R:\hat\phi(0,n)=0$ for all $n\in Z \ 0$ and $||\phi||_{E^1
(T^2)}=||\hat{\phi}(m,n)(1+|m|+|n/m|)||_{l^2(Z^2)}<\infty$.

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