Existence and uniqueness of minimal blow-up solutions to an inhomogeneous mass critical NLS

DOI10.1090/S0894-0347-2010-00688-1zbMath1218.35226arXiv1001.1627OpenAlexW2024449135MaRDI QIDQ5390540

Jérémie Szeftel, Pierre Raphaël

Publication date: 4 April 2011

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1001.1627

zbMATH Keywords

nonlinear Schrödinger equationblow-upfocusingcritical mass

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) NLS equations (nonlinear Schrödinger equations) (35Q55) Blow-up in context of PDEs (35B44) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items

Nondispersive solutions to the mass critical half-wave equation in two dimensions, On Pseudoconformal Blow-Up Solutions to the Self-Dual Chern-Simons-Schrödinger Equation: Existence, Uniqueness, and Instability, An asymptotic expansion of two-bubble wave maps in high equivariance classes, Blowup of \(H^1\) solutions for a class of the focusing inhomogeneous nonlinear Schrödinger equation, A semi-linear energy critical wave equation with an application, Blow-up dynamics for the self-dual Chern-Simons-Schrödinger equation, Construction of type II blow-up solutions for the energy-critical wave equation in dimension 5, Sharp condition for inhomogeneous nonlinear Schrödinger equations by cross-invariant manifolds, A two-soliton with transient turbulent regime for the cubic half-wave equation on the real line, Blowup dynamics for smooth data equivariant solutions to the critical Schrödinger map problem, Construction of a minimal mass blow up solution of the modified Benjamin-Ono equation, Two-bubble dynamics for threshold solutions to the wave maps equation, On well posedness for the inhomogeneous nonlinear Schrödinger equation, Construction of Multibubble Solutions for the Critical GKDV Equation, Scattering for the radial focusing inhomogeneous NLS equation in higher dimensions, Construction of multi-bubble solutions for the energy-critical wave equation in dimension 5, Uniqueness of <scp>Two‐Bubble</scp> Wave Maps in High Equivariance Classes, Global dynamics for a class of inhomogeneous nonlinear Schrödinger equations with potential, Soliton resolution for the energy-critical nonlinear wave equation in the radial case, Nonflat conformal blow-up profiles for the 1-dimensional critical nonlinear Schrödinger equation, Finite time/infinite time blow-up behaviors for the inhomogeneous nonlinear Schrödinger equation, Full family of flattening solitary waves for the critical generalized KdV equation, Dynamics of two interacting kinks for the \(\phi^6\) model, Strongly interacting multi-solitons with logarithmic relative distance for the gKdV equation, Minimal mass blow-up solutions for nonlinear Schrödinger equations with a potential, Scattering theory in weighted L2 space for a class of the defocusing inhomogeneous nonlinear Schrödinger equation, Standing waves with prescribed \(L^2\)-norm to nonlinear Schrödinger equations with combined inhomogeneous nonlinearities, Multi-bubble Bourgain-Wang solutions to nonlinear Schrödinger equations, Minimal Mass Blow-Up Solutions for the \(\boldsymbol{L}^{\boldsymbol{2}}\)-Critical NLS with the Delta Potential for Even Data in One Dimension, Blow up dynamics for smooth equivariant solutions to the energy critical Schrödinger map, Nondispersive solutions to the \(L ^{2}\)-critical half-wave equation, Threshold for blowup and stability for nonlinear Schrödinger equation with rotation, On collapsing ring blow-up solutions to the mass supercritical nonlinear Schrödinger equation, Existence of multi-solitary waves with logarithmic relative distances for the NLS equation, Unnamed Item, Minimal-mass blow-up solutions for nonlinear Schrödinger equations with an inverse potential, Blow-up solutions to nonlinear Schrödinger system at multiple points, Classification of minimal mass blow-up solutions for an \({L^{2}}\) critical inhomogeneous NLS, Stable Blowup Dynamics for the 1‐Corotational Energy Critical Harmonic Heat Flow, Minimal mass blow-up solutions for the \(L^2\) critical NLS with inverse-square potential, Construction of two-bubble solutions for some energy-critical wave equations, Sharp asymptotics for the minimal mass blow up solution of the critical gKdV equation, Dynamics near the ground state for the energy critical nonlinear heat equation in large dimensions, Minimal blow-up solutions of mass-critical inhomogeneous Hartree equation, Stable self-similar blow-up dynamics for slightly \(L^2\)-supercritical generalized KdV equations, Finite-time blowup for a Schrödinger equation with nonlinear source term, Energy scattering for a class of the defocusing inhomogeneous nonlinear Schrödinger equation, Blow up for the critical generalized Korteweg-de Vries equation. I: Dynamics near the soliton, Long Time Dynamics of Nonradial Solutions to Inhomogeneous Nonlinear Schrödinger Equations, Blowup dynamics for mass critical half-wave equation in 3D, Bilinear Strichartz's type estimates in Besov spaces with application to inhomogeneous nonlinear biharmonic Schrödinger equation, Unnamed Item, Homogenization for the cubic nonlinear Schrödinger equation on R2, Construction of 2-solitons with logarithmic distance for the one-dimensional cubic Schrödinger system, Strongly interacting kink-antikink pairs for the scalar field equation in dimension \(1+1\), Ground state of the mass-critical inhomogeneous nonlinear Schrödinger functional, A compactness result for inhomogeneous nonlinear Schrödinger equations, Threshold dynamics for corotational wave maps, Well-posedness and scattering of inhomogeneous cubic-quintic NLS, Energy critical Schrödinger equation with weighted exponential nonlinearity: Local and global well-posedness, Small data global well-posedness and scattering for the inhomogeneous nonlinear Schrödinger equation in \(H^s (\mathbb{R}^n)\), Solutions blowing up on any given compact set for the energy subcritical wave equation, Energy scattering for a class of inhomogeneous nonlinear Schrödinger equation in two dimensions, Small data scattering of the inhomogeneous cubic-quintic NLS in 2 dimensions, Dynamics of some coupled nonlinear Schrödinger systems in, Limit of the blow-up solution for the inhomogeneous nonlinear Schrödinger equation, Dynamics of strongly interacting kink-antikink pairs for scalar fields on a line, Construction of minimal mass blow-up solutions to rough nonlinear Schrödinger equations, On uniqueness of multi-bubble blow-up solutions and multi-solitons to \(L^2\)-critical nonlinear Schrödinger equations, Blow up and near soliton dynamics for the \(L^2\) critical gKdV equation, Dispersive estimates for scalar and matrix Schrödinger operators on \(\mathbb H^{n+1}\), Global well-posedness and blow-up on the energy space for the inhomogeneous nonlinear Schrödinger equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On stability of pseudo-conformal blowup for \(L^{2}\)-critical Hartree NLS
• Stable blow up dynamics for the critical co-rotational wave maps and equivariant Yang-Mills problems
• Nonlinear Schrödinger equations and sharp interpolation estimates
• Dynamic of threshold solutions for energy-critical NLS
• Global well-posedness, scattering and blow-up for the energy-critical, focusing, nonlinear Schrö\-dinger equation in the radial case
• Multi solitary waves for nonlinear Schrödinger equations
• Construction of solutions with exactly k blow-up points for the Schrödinger equation with critical nonlinearity
• Non-generic blow-up solutions for the critical focusing NLS in 1-D
• Uniqueness of positive solutions of \(\Delta u-u+u^ p=0\) in \(R^ n\)
• Symmetry and related properties via the maximum principle
• Determination of blow-up solutions with minimal mass for nonlinear Schrödinger equations with critical power
• On a class of nonlinear Schrödinger equations. I. The Cauchy problem, general case
• Nonexistence of blow-up solution with minimal \(L^2\)-mass for the critical gKdV equation
• Two singular dynamics of the nonlinear Schrödinger equation on a plane domain
• Sharp upper bound on the blow-up rate for the critical nonlinear Schrödinger equation
• Stability of blow-up profile and lower bounds for blow-up rate for the critical generalized KdV equation
• Stability of the log-log bound for blow up solutions to the critical nonlinear Schrödinger equation
• On universality of blow up profile for \(L^2\) critical nonlinear Schrödinger equation
• The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation
• Existence and stability of the log-log blow-up dynamics for the \(L^2\)-critical nonlinear Schrödinger equation in a domain
• Proof of a spectral property related to the singularity formation for the \(L^{2}\) critical nonlinear Schrödinger equation
• Minimal Blow-Up Solutions to the Mass-Critical Inhomogeneous NLS Equation
• Two-soliton solutions to the three-dimensional gravitational Hartree equation
• Spectra of Linearized Operators for NLS Solitary Waves
• Infinite time aggregation for the critical Patlak‐Keller‐Segel model in ℝ²
• Lyapunov stability of ground states of nonlinear dispersive evolution equations
• Characterization of Minimal-Mass Blowup Solutions to the Focusing Mass-Critical NLS
• On a sharp lower bound on the blow-up rate for the 𝐿² critical nonlinear Schrödinger equation
• Asymptotic N -soliton-like solutions of the subcritical and critical generalized Korteweg-de Vries equations