On the low regularity of the fifth order Kadomtsev-Petviashvili I equation

Details On the low regularity of the fifth order Kadomtsev-Petviashvili I equation On the low regularity of the fifth order Kadomtsev-Petviashvili I equation

2007-09-02

arxiv.org/abs/0709.0103v2

J. Differential Equations 245 (2008) 3433-3469

Mathematics

Analysis of PDEs

30pages

Scientific paper

10.1016/j.jde.2008.07.005

We consider the fifth order Kadomtsev-Petviashvili I (KP-I) equation as $\partial_tu+\alpha\partial_x^3u+\partial^5_xu+\partial_x^{-1}\partial_y^2u+uu_x=0,$ while $\alpha\in \mathbb{R}$. We introduce an interpolated energy space $E_s$ to consider the well-posedeness of the initial value problem (IVP) of the fifth order KP-I equation. We obtain the local well-posedness of IVP of the fifth order KP-I equation in $E_s$ for $0

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