On the Davey-Stewartson system with competing nonlinearities

DOI10.1063/1.4942633zbMath1351.35156OpenAlexW2330746540MaRDI QIDQ2798662

Shihui Zhu

Publication date: 13 April 2016

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.4942633

zbMATH Keywords

nonlinearitiesDavey-Stewartson systemblow-up and global existence of solutions

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) NLS equations (nonlinear Schrödinger equations) (35Q55) Blow-up in context of PDEs (35B44)

Related Items (13)

Dynamics of blow-up solutions for the Schrödinger-Choquard equation ⋮ Finite time blow-up for the nonlinear Schrödinger equation in trapped dipolar quantum gases with arbitrarily positive initial energy ⋮ On finite time blow-up for a 3D Davey-Stewartson system ⋮ On the blow-up solutions for the fractional nonlinear Schrödinger equation with combined power-type nonlinearities ⋮ Blowup results and concentration in focusing Schrödinger-Hartree equation ⋮ Unnamed Item ⋮ Stability of standing waves for the fractional Schrödinger-Choquard equation ⋮ On the blow-up solutions for the nonlinear Schrödinger equation with combined power-type nonlinearities ⋮ Blow-up in several points for the Davey-Stewartson system in \(\mathbb{R}^2\) ⋮ Small solitons and multisolitons in the generalized Davey-Stewartson system ⋮ Instability of standing waves for the nonlinear Schrödinger-Poisson equation in the \(L^2\)-critical case ⋮ Existence, stability and asymptotic behaviour of normalized solutions for the Davey-Stewartson system ⋮ Sharp thresholds of blow-up and global existence for the Schrödinger equation with combined power-type and Choquard-type nonlinearities

Cites Work

• Unnamed Item
• Sharp blow-up criteria for the Davey-Stewartson system in \(\mathbb R^3\)
• The sharp threshold and limiting profile of blow-up solutions for a Davey-Stewartson system
• Mass concentration for the Davey-Stewartson system.
• Nonlinear Schrödinger equations and sharp interpolation estimates
• Sharp threshold of global existence and instability of standing wave for a Davey-Stewartson system
• The nonlinear Schrödinger equation. Self-focusing and wave collapse
• Decay of weak solutions to the Davey-Stewartson systems
• Stability of standing waves for the generalized Davey-Stewartson system
• The focusing singularity of the Davey-Stewartson equations for gravity- capillary surface waves
• A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
• On the initial value problem for the Davey-Stewartson systems
• On the structure and formation of singularities in solutions to nonlinear dispersive evolution equations
• Exact blow-up solutions to the Cauchy problem for the Davey–Stewartson systems
• On the existence of standing waves for a davey–stewartson system
• On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations
• Description of the lack of compactness for the Sobolev imbedding
• The Cauchy problem for Davey-Stewartson systems
• Global existence and nonexistence results for a generalized Davey–Stewartson system
• On three-dimensional packets of surface waves
• Sharp conditions of global existence for the generalized Davey–Stewartson system

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