Well-posedness for the Kadomtsev-Petviashvili II equation and generalisations

Details Well-posedness for the Kadomtsev-Petviashvili II equation and generalisations Well-posedness for the Kadomtsev-Petviashvili II equation and generalisations

2006-11-07

arxiv.org/abs/math/0611197v1

Mathematics

Analysis of PDEs

17 pages

Scientific paper

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 H^{s_1,s_2}(R^2) with s_1 > -1/2 and s_2 \geq 0. On the H^{s_1,0}(R^2) 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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