Well-posedness for the Kadomtsev-Petviashvili II equation and generalisations
M. Hadac
Abstract
We show the local in time well-posedness of the Cauchy problem for the Kadomtsev-Petviashvili II equation for initial data in the non-isotropic Sobolev space Hs1,s2(R2) with s1 > -1/2 and s2 ≥ 0. On the Hs1,0(R2) scale this result includes the full subcritical range without any additional low frequency assumption on the initial data. More generally, we prove the local in time well-posedness of the Cauchy problem for a dispersion generalised KP II type equation. We also deduce a global well-posedness result for the generalised equation.
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