Blow-up for the 1D cubic NLS
From MaRDI portal
Publication:6188094
DOI10.1007/s00220-023-04906-3arXiv2304.11050OpenAlexW4391164668WikidataQ129511332 ScholiaQ129511332MaRDI QIDQ6188094
Nickolay Tzvetkov, Renato Lucà, Valeria Banica, Luis Vega
Publication date: 1 February 2024
Published in: Communications in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2304.11050
Asymptotic behavior of solutions to PDEs (35B40) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) NLS equations (nonlinear Schrödinger equations) (35Q55) Blow-up in context of PDEs (35B44) Time-dependent Schrödinger equations and Dirac equations (35Q41)
Cites Work
- Unnamed Item
- Unnamed Item
- Bounds on the growth of high Sobolev norms of solutions to nonlinear Schrödinger equations on \(S^1\).
- A new proof of long-range scattering for critical nonlinear Schrödinger equations.
- On the vortex filament conjecture for Euler flows
- Well-posedness of the Cauchy problem for the Korteweg-de Vries equation at the critical regularity.
- Scattering for 1D cubic NLS and singular vortex dynamics
- On the stability of a singular vortex dynamics
- The global Cauchy problem for the nonlinear Schrödinger equation revisited
- Long range scattering for nonlinear Schrödinger equations in one space dimension
- Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
- Geometric optics and long range scattering for one-dimensional nonlinear Schrödinger equations
- Global wellposedness for 1D nonlinear Schrödinger equation for data with an infinite \(L^2\) norm
- Conserved energies for the cubic nonlinear Schrödinger equation in one dimension
- On the ill-posedness of some canonical dispersive equations.
- On the one dimensional cubic NLS in a critical space
- Low regularity conservation laws for integrable PDE
- Stability of the self-similar dynamics of a vortex filament
- Evolution of polygonal lines by the binormal flow
- Dispersive Partial Differential Equations
- 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
- The cauchy problem for the critical nonlinear Schrödinger equation in Hs
- Asymptotics for large time of solutions to the nonlinear Schrodinger and Hartree equations
- On uniqueness and continuation properties after blow‐up time of self‐similar solutions of nonlinear schrödinger equation with critical exponent and critical mass
- Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocusing equations
- A Remark on Norm Inflation with General Initial Data for the Cubic Nonlinear Schrödinger Equations in Negative Sobolev Spaces
- Norm-inflation with Infinite Loss of Regularity for Periodic NLS Equations in Negative Sobolev Spaces
- Formation of Singularities and Self-Similar Vortex Motion Under the Localized Induction Approximation†
- A soliton on a vortex filament
- Transport of Gaussian measures under the flow of one-dimensional fractional nonlinear Schrödinger equations
- Large-Data Equicontinuity for the Derivative NLS
This page was built for publication: Blow-up for the 1D cubic NLS
