Global analysis for rough solutions to the Davey-Stewartson system
type: Item
instance of: scholarly article
title: Global analysis for rough solutions to the Davey-Stewartson system
zbMATH Open document ID: 1257.35154
DOI: 10.1155/2012/578701
author: Yanyan Li
published in: Abstract and Applied Analysis
publication date: 2013-02-04T00:00:00Z
review text: Summary: The global well-posedness of rough solutions to the Cauchy problem for the Davey-Stewartson system is obtained. It reads that if the initial data is in \(H^s\) with \(s > 2/5\), then there exists a global solution in time, and the \(H^s\) norm of the solution obeys polynomial-in-time bounds. The new ingredient in this paper is an interaction Morawetz estimate, which generates a new space-time \(L^4_{t,x}\) estimate for nonlinear equation with the relatively general defocusing power nonlinearity.
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 35A02
Mathematics Subject Classification ID: 35C11
zbMATH DE Number: 6134117
Wikidata QID: Q58695584
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/578701
OpenAlex ID: W2103093230
cites work: On three-dimensional packets of surface waves
cites work: On the initial value problem for the Davey-Stewartson systems
cites work: Local existence in time of small solutions to the elliptic-hyperbolic Davey-Stewartson system in the usual Sobolev space
cites work: Decay of weak solutions to the Davey-Stewartson systems
cites work: Global existence of small solutions to the Davey-Stewartson and the Ishimori systems
cites work: On the Davey-Stewartson systems
cites work: The Cauchy problem for Davey-Stewartson systems
cites work: Sharp conditions of global existence for the generalized Davey–Stewartson system
cites work: Sharp threshold of global existence and instability of standing wave for a Davey-Stewartson system
cites work: Sharp blow-up criteria for the Davey-Stewartson system in \(\mathbb R^3\)
cites work: The nonlinear Schrödinger equation. Self-focusing and wave collapse
cites work: Mass concentration for the Davey-Stewartson system.
cites work: The sharp threshold and limiting profile of blow-up solutions for a Davey-Stewartson system
cites work: Two-dimensional wave packets in an elastic solid with couple stresses
cites work: Global existence and nonexistence results for a generalized Davey–Stewartson system
cites work: Standing waves for a generalized Davey–Stewartson system
cites work: Focusing and defocusing cases of the purely elliptic generalized Davey-Stewartson system
cites work: Q4393968
cites work: Global well-posedness for semi-linear wave equations
cites work: Global well-posedness for the modified korteweg-de vries equation
cites work: Q4335085
cites work: The Global Cauchy Problem in Bourgain's-Type Spaces for a Dispersive Dissipative Semilinear Equation
cites work: Global well-posedness below energy space for the \(1\)-dimensional Zakharov system
cites work: \(H^{s}\)-global well-posedness for semilinear wave equations
cites work: Almost conservation laws and global rough solutions to a nonlinear Schrödinger equation.
cites work: Improved Interaction Morawetz Inequalities for the Cubic Nonlinear Schrödinger Equation on ℝ2
cites work: Almost conservation law and global rough solutions to a nonlinear Davey-Stewartson equation
cites work: Global well-posedness and scattering for the defocusing, \(L^2\)-critical nonlinear Schrödinger equation when \(d \geq 3\)
cites work: Global existence and scattering for rough solutions of a nonlinear Schrödinger equation on ℝ3
cites work: Ground state mass concentration in the \(L^2\)-critical nonlinear Schrödinger equation below \(H^1\)
cites work: Decay and scattering of solutions of a nonlinear Schrödinger equation
cites work: ON THE GLOBAL EXISTENCE OF ROUGH SOLUTIONS OF THE CUBIC DEFOCUSING SCHRÖDINGER EQUATION IN R2 + 1
description: scientific article; zbMATH DE number 6134117