On the existence of global solutions of the Hartree equation for initial data in the modulation space \(M^{p , q}(\mathbb{R})\)
type: Item
instance of: scholarly article
title: On the existence of global solutions of the Hartree equation for initial data in the modulation space \(M^{p , q}(\mathbb{R})\)
zbMATH Open document ID: 1487.35352
author: Ramesh Manna
published in: Journal of Differential Equations
publication date: 2022-03-04T00:00:00Z
review text: The author studies the Cauchy problem for Hartree type equations, defined as Schrödinger equations with nonlinear potential involving cubic powers and convolutions with a singular kernel, cf. \textit{P. Cao} and \textit{R. Carles} [Rev. Math. Phys. 23, No. 9, 933--967 (2011; Zbl 1239.35145)]. A global existence and uniqueness result is obtained in the frame of the modulation spaces of \textit{H. G. Feichtinger} and \textit{G. Narimani} [Appl. Comput. Harmon. Anal. 21, No. 3, 349--359 (2006; Zbl 1106.42005)], for large initial data. The proof is based on a splitting method, by decomposing the initial datum as a sum of a square integrable function and a function in modulation spaces. The paper gives evidence of the effectiveness of the use of modulation spaces in the study of nonlinear problems.
reviewed by: Luigi Rodino
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 42B35
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 35A02
zbMATH DE Number: 7483918
zbMATH Keywords: nonlinear Hartree equation
zbMATH Keywords: global well-posedness
zbMATH Keywords: modulation spaces
MaRDI profile type: Publication
full work available at URL: j.jde.2022.02.003
OpenAlex ID: W4211153332
cites work: Local well-posedness of nonlinear dispersive equations on modulation spaces
cites work: Global wellposedness of defocusing critical nonlinear Schrödinger equation in the radial case
cites work: Semi-classical wave packet dynamics for Hartree equations
cites work: On the Cauchy problem for the Hartree type equation in the Wiener algebra
cites work: Global existence of solutions to the Cauchy problem for time-dependent Hartree equations
cites work: On the existence of global solutions of the one-dimensional cubic NLS for initial data in the modulation space \(M_{p, q}(\mathbb{R})\)
cites work: Asymptotic estimates for unimodular Fourier multipliers on modulation spaces
cites work: Remarks on Fourier multipliers and applications to the wave equation
cites work: Sparsity of Gabor representation of Schrödinger propagators
cites work: The Cauchy problem for the Hartree type equation in modulation spaces
cites work: Fourier multipliers of classical modulation spaces
cites work: On a class of non linear Schrödinger equations with non local interactions
cites work: Foundations of time-frequency analysis
cites work: Q5717221
cites work: On the 1D cubic nonlinear Schrödinger equation in an almost critical space
cites work: Stability of nonlinear Schrödinger equations on modulation spaces
cites work: On the global well-posedness for the nonlinear Schrödinger equations with large initial data of infinite \(L^2\) norm
cites work: On existence of global solutions of Schrödinger equations with subcritical nonlinearity for \(\widehat L^p\)-initial data
cites work: Q4309712
cites work: The global Cauchy problems for the nonlinear dispersive equations on modulation spaces
cites work: Endpoint Strichartz estimates
cites work: Modulation spaces and non-linear Hartree type equations
cites work: The Cauchy problem for nonlinear Schrödinger equations in modulation spaces
cites work: Modulation Spaces and Nonlinear Evolution Equations
cites work: Continuity properties for modulation spaces, with applications to pseudo-differential calculus. I.
cites work: Q3779084
cites work: Global wellposedness for 1D nonlinear Schrödinger equation for data with an infinite \(L^2\) norm
cites work: The global Cauchy problem for the NLS and NLKG with small rough data
cites work: Isometric decomposition operators, function spaces \(E_{p,q}^{\lambda}\) and applications to nonlinear evolution equations
cites work: Q3009497
DOI: 10.1016/J.JDE.2022.02.003
description: scientific article; zbMATH DE number 7483918