Sebastian Herr, Akansha Sanwal, Robert Schippa
Published 2022-12-28Version 1
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.
Low regularity well-posedness for KP-I equations: the dispersion generalised case
Low regularity well-posedness of nonlocal dispersive perturbations of Burgers' equation
Remark on the low regularity well-posedness of the KP-I equation
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