On the sharp scattering threshold for the mass-energy double critical nonlinear Schrödinger equation via double track profile decomposition

DOI10.4171/AIHPC/71arXiv2108.00915OpenAlexW4316036350MaRDI QIDQ6200392

Yongming Luo

Publication date: 22 March 2024

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2108.00915

zbMATH Keywords

combined nonlinearitiesscattering thresholddouble critical Schrödinger equation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Scattering theory for PDEs (35P25) NLS equations (nonlinear Schrödinger equations) (35Q55) Blow-up in context of PDEs (35B44) Soliton solutions (35C08) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Long time dynamics of the 3D radial NLS with the combined terms
• Global well-posedness and scattering for the defocusing, \(L^2\)-critical, nonlinear Schrödinger equation when \(d=2\)
• Solitons and scattering for the cubic-quintic nonlinear Schrödinger equation on \({\mathbb{R}^3}\)
• Nonlinear scalar field equations. II: Existence of infinitely many solutions
• Nonlinear Schrödinger equations and sharp interpolation estimates
• Nonlinear scalar field equations. I: Existence of a ground state
• On the Cauchy problem of 3D energy-critical Schrödinger equations with subcritical perturbations
• Global well-posedness, scattering and blow-up for the energy-critical, focusing, nonlinear Schrö\-dinger equation in the radial case
• Global well-posedness and scattering for the mass critical nonlinear Schrödinger equation with mass below the mass of the ground state
• Focusing and multi-focusing solutions of the nonlinear Schrödinger equation
• Stability of the soliton-like ``bubbles
• Scattering for the nonradial 3D cubic nonlinear Schrödinger equation
• Uniqueness of positive solutions of \(\Delta u-u+u^ p=0\) in \(R^ n\)
• On the 4D nonlinear Schrödinger equation with combined terms under the energy threshold
• The dynamics of the 3D radial NLS with the combined terms
• Existence of a ground state and scattering for a nonlinear Schrödinger equation with critical growth
• Scattering threshold for the focusing nonlinear Klein-Gordon equation
• On scattering for the cubic defocusing nonlinear Schrödinger equation on the waveguide \(\mathbb{R}^2 \times \mathbb{T}\)
• Sharp scattering for the cubic-quintic nonlinear Schrödinger equation in the focusing-focusing regime
• Normalized solutions for Schrödinger equations with critical Sobolev exponent and mixed nonlinearities
• Normalized ground states for the NLS equation with combined nonlinearities: the Sobolev critical case
• Scattering for the mass super-critical perturbations of the mass critical nonlinear Schrödinger equations
• The defocusing energy-critical nonlinear Schrödinger equation in higher dimensions
• Global well-posedness and scattering for the energy-critical Schrödinger equation in \(\mathbb R^{3}\)
• Global well-posedness and scattering for nonlinear Schrödinger equations with combined nonlinearities in the radial case
• Global well-posedness and scattering for the defocusing, L2-critical, nonlinear Schrödinger equation when d = 1
• Existence and instability of standing waves with prescribed norm for a class of Schrödinger-Poisson equations
• Global well-posedness and scattering for the defocusing, $L^{2}$-critical nonlinear Schrödinger equation when $d ≥3$
• The dynamics of the NLS with the combined terms in five and higher dimensions
• The cauchy problem for the critical nonlinear Schrödinger equation in Hs
• Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equation in R 1+4
• The focusing energy-critical nonlinear Schrödinger equation in dimensions five and higher
• On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations
• Endpoint Strichartz estimates
• Global wellposedness of defocusing critical nonlinear Schrödinger equation in the radial case
• Global well-posedness and scattering for the focusing, cubic Schrödinger equation in dimension d=4
• Threshold scattering for the 2D radial cubic-quintic NLS
• Orbital stability vs. scattering in the cubic-quintic Schrödinger equation
• Scattering for the Cubic-Quintic NLS: Crossing the Virial Threshold
• The Nonlinear Schrödinger Equation with Combined Power-Type Nonlinearities
• Simulation of instability of bright solitons for NLS with saturating nonlinearity
• On ground state (in-)stability in multi-dimensional cubic-quintic Schrödinger equations

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