Work

Global Results for Weakly Dispersive KP-II Equations on the Cylinder

Year: 2026

Type: article

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 in hand, we show that global well-posedness of the quasilinear Cauchy problem in $$L^2(\mathbb {R}\times \mathbb {T})$$ L 2 ( R × T ) . Finally, we prove a long-time decay property of solutions with small mass by using the Kato smoothing effect in the fractional case.

Source: Archive for Rational Mechanics and Analysis

DOI: 10.1007/s00205-026-02208-1

Authors: Sebastian Herr, Robert Schippa, Nikolay Tzvetkov

Institutions: Bielefeld University, University of Bonn, École Normale Supérieure de Lyon, Centre National de la Recherche Scientifique, Unité de Mathématiques Pures et Appliquées

Language: English

Topic: Advanced Mathematical Physics Problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090