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

DOI10.1016/j.jfa.2023.110292arXiv2212.14067OpenAlexW4389579091MaRDI QIDQ6185662

Akansha Sanwal, Sebastian Herr, Robert Schippa

Publication date: 30 January 2024

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2212.14067

zbMATH Keywords

KP equationlocal well-posednessshort-time Fourier restriction norm method

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Maximal functions, Littlewood-Paley theory (42B25) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Fourier integral operators applied to PDEs (35S30) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Global well-posedness of the KP-I initial-value problem in the energy space
• Erratum to ``Well-posedness and scattering for the KP-II equation in a critical space [Ann. I. H. Poincaré - AN 26 (3) (2009) 917-941]
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
• Well-posedness and ill-posedness results for the Kadomtsev-Petviashvili-I equation
• Multilinear Calderón-Zygmund theory
• Global well-posedness for the KP-I equation
• Numerical study of blow up and stability of solutions of generalized Kadomtsev-Petviashvili equations
• Global well-posedness for the KP-I equation on the background of a non-localized solution
• The KdV/KP-I Limit of the Nonlinear Schrödinger Equation
• Non-Existence of Solutions for the Periodic Cubic NLS below ${L}^{{2}}$
• Dispersive Perturbations of Burgers and Hyperbolic Equations I: Local Theory
• Local well-posedness for quasi-linear problems: A primer
• On 2D nonlinear Schrödinger equations with data on \(\mathbb{R} \times \mathbb{T}\)
• Global regularity of wave maps. II: Small energy in two dimensions
• Low regularity well-posedness for KP-I equations: the dispersion-generalized case

This page was built for publication: Low regularity well-posedness of KP-I equations: the three-dimensional case