Junfeng Li


"On the low regularity of the fifth order Kadomtsev-Petiashvili I
equation"


 We consider the fifth order Kadomtsev-Petviashvili I (KP-I) equation.
We introduce an energy space which is a nature function space to
consider the well-posedeness of the initial problem (IVP) of the fifth
order KP-I equation. For the third order KP- I equation, it has been
proved that one can not obtain the well-posedness in the Energy space
by using the Picard interation argument. We will present that the
Picard interation argument work in our case. Since the fifth order
dispersive function can help us to recover a full derivative while in
the third KP-I equation, one can only recover a half derivative. We
obtain the local well-posedness of IVP of the fifth order KP-I
equation in some low regularity energy space and global well-posedness
for the general energy space.