Global results for weakly dispersive KP-II equations on the cylinder

2025/04/12 by Herr, Sebastian, Schippa, Robert, Tzvetkov, Nikolay · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.09333

Abstract

We consider the dispersion-generalized KP-II equation on a partially periodic domain in the weakly dispersive regime. We use Fourier decoupling techniques to derive essentially sharp Strichartz estimates. With these at hand, we show global well-posedness of the quasilinear Cauchy problem in L²(ℝ × \mathbbT). Finally, we prove a long-time decay property of solutions with small mass by using the Kato smoothing effect in the fractional case.

Cited by

• Sharp L⁴ Strichartz estimate for Hyperbolic Schrödinger equation on ℝ× \mathbbT

Related

• Improved well-posedness for quasilinear and sharp local well-posedness for semilinear KP-I equations
• Global solutions to the dissipative quasi-geostrophic equation with dispersive forcing
• Well-posedness for the Kadomtsev-Petviashvili II equation and generalisations
• Dispersive Decay Bound of Small Data Solutions to Kawahara Equation in a Finite Time Scale
• The Cauchy problem for the periodic Kadomtsev--Petviashvili--II equation below L²