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

TL;DR

This paper establishes low regularity local well-posedness results for the 3D KP-I equations across various settings, using bilinear and energy estimates in weak dispersion regimes.

Contribution

It extends well-posedness results of KP-I equations to three dimensions with low regularity initial data, considering diverse spatial configurations and dispersion relations.

Findings

Well-posedness in low regularity spaces for 3D KP-I

Applicability to periodic, non-periodic, and mixed settings

Use of bilinear and energy estimates in weak dispersion regime

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.