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

Abstract

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.

36 pages

References in corpus (3)

• Global well-posedness of the KP-I initial-value problem in the energy space
• Global well-posedness for the KP-I equation on the background of a non localized solution
• Low regularity well-posedness for KP-I equations: the dispersion-generalized case