Low regularity well-posedness of KP-I equations: the three-dimensional case

In this paper, low regularity local well-posedness results for the Kadomtsev–Petviashvili–I equation posed in spatial dimension $d=3$ are proved. Periodic, non-periodic and mixed settings as well as generalized dispersion relations are considered. In the weak dispersion regime, these initial value problems show a quasilinear behavior so that bilinear and energy estimates on frequency dependent time scales are used in the analysis.