Recent progress on multi-bubble blow-ups and multi-solitons to (stochastic) focusing nonlinear Schrödinger equations

DOI10.1007/s10013-023-00640-4zbMath1543.35215MaRDI QIDQ6570531

Viorel Barbu, Michael Roeckner, Deng Zhang

Publication date: 10 July 2024

Published in: Vietnam Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

uniquenessnonlinear Schrödinger equationmulti-solitonsmulti-bubble blow-ups

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Existence problems for PDEs: global existence, local existence, non-existence (35A01) PDEs with randomness, stochastic partial differential equations (35R60) Blow-up in context of PDEs (35B44) Soliton solutions (35C08) Time-dependent Schrödinger equations and Dirac equations (35Q41) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Stochastic nonlinear Schrödinger equations
• The stochastic logarithmic Schrödinger equation
• The Cauchy problem for quasi-linear Schrödinger equations
• Stochastic nonlinear Schrödinger equations with linear multiplicative noise: rescaling approach
• L\({}^ 2\) concentration of blow-up solutions for the nonlinear Schrödinger equation with critical power nonlinearity
• Nonlinear Schrödinger equations and sharp interpolation estimates
• The general quasilinear ultrahyperbolic Schrödinger equation
• 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
• Global well-posedness and scattering for the mass critical nonlinear Schrödinger equation with mass below the mass of the ground state
• Construction of solutions with exactly k blow-up points for the Schrödinger equation with critical nonlinearity
• Strichartz estimates and local smoothing estimates for asymptotically flat Schrödinger equations
• Quantum trajectories and measurements in continuous time. The diffusive case
• Blow-up phenomena for critical nonlinear Schrödinger and Zakharov equations
• Optical turbulence: weak turbulence, condensates and collapsing filaments in the nonlinear Schrödinger equation
• Determination of blow-up solutions with minimal mass for nonlinear Schrödinger equations with critical power
• The nonlinear Schrödinger equation. Self-focusing and wave collapse
• Attractors for random dynamical systems
• Sharp upper bound on the blow-up rate for the critical nonlinear Schrödinger equation
• Numerical resolution of stochastic focusing NLS equations
• Optimal bilinear control of nonlinear stochastic Schrödinger equations driven by linear multiplicative noise
• \(\log\)-\(\log\) blow up solutions blow up at exactly \(m\) points
• Recent progress on stochastic nonlinear Schrödinger equations
• Profiles for the radial focusing \(4d\) energy-critical wave equation
• Profiles and quantization of the blow up mass for critical nonlinear Schrödinger equation
• Blowup for the stochastic nonlinear Schrödinger equation with multiplicative noise
• A stochastic nonlinear Schrödinger equation with multiplicative noise
• On the effect of a noise on the solutions of the focusing supercritical nonlinear Schrödinger equation
• On universality of blow up profile for \(L^2\) critical nonlinear Schrödinger equation
• Controlling rough paths
• Behavior of solutions to the 1D focusing stochastic nonlinear Schrödinger equation with spatially correlated noise
• A note on log-log blow up solutions for stochastic nonlinear Schrödinger equations
• 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
• Global well-posedness for the defocussing mass-critical stochastic nonlinear Schrödinger equation on \(\mathbb{R}\) at \(L^2\) regularity
• Optimal bilinear control of stochastic nonlinear Schrödinger equations: mass-(sub)critical case
• The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation
• Soliton resolution along a sequence of times for the focusing energy critical wave equation
• Stochastic nonlinear Schrödinger equations: no blow-up in the non-conservative case
• Scattering for stochastic nonlinear Schrödinger equations
• Classification of the radial solutions of the focusing, energy-critical wave equation
• Stability in \(H^1\) of the sum of \(K\) solitary waves for some nonlinear Schrödinger equations
• On the stochastic Strichartz estimates and the stochastic nonlinear Schrödinger equation on a compact Riemannian manifold
• A determination of the blowup solutions to the focusing NLS with mass equal to the mass of the soliton
• The instability of Bourgain-Wang solutions for the <i>L</i><sup xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> critical NLS
• Infinite soliton and kink-soliton trains for nonlinear Schrödinger equations
• Multi-Soliton Solutions for the Supercritical gKdV Equations
• Rate of L2 concentration of blow-up solutions for the nonlinear schrödinger equation with critical power
• On the structure and formation of singularities in solutions to nonlinear dispersive evolution equations
• Foundations of Modern Probability
• The Stochastic Nonlinear Schrödinger Equation inH¹
• White noise in the two-dimensional nonlinear schrödinger equation
• On smoothness and uniqueness of multi-solitons of the non-linear Schrödinger equations
• Strichartz and Local Smoothing Estimates for Stochastic Dispersive Equations with Linear Multiplicative Noise
• Behaviour of solutions to the 1D focusing stochastic L2-critical and supercritical nonlinear Schrödinger equation with space-time white noise
• INTERACTION OF SOLITONS FROM THE PDE POINT OF VIEW
• Existence and uniqueness of minimal blow-up solutions to an inhomogeneous 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
• Fast-moving finite and infinite trains of solitons for nonlinear Schrödinger equations
• A course on rough paths. With an introduction to regularity structures
• On the formation of singularities in solutions of the critical nonlinear Schrödinger equation
• Numerical simulation of focusing stochastic nonlinear Schrödinger equations
• Multi solitary waves to stochastic nonlinear Schrödinger equations

This page was built for publication: Recent progress on multi-bubble blow-ups and multi-solitons to (stochastic) focusing nonlinear Schrödinger equations