Nonlinear fractional Schrödinger equations in one dimension

2013/10/07 by Alexandru D. Ionescu, Fabio Pusateri · 196 citations
Mathematics · #Advanced Mathematical Physics Problems #Applied mathematics #Dimension (graph theory) #Fractional Differential Equations Solutions #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear system #Numerical methods in inverse problems #Physics #Pure mathematics #Quantum mechanics

paper · pdf · doi:10.1016/j.jfa.2013.08.027

published in Journal of Functional Analysis 266(1), 139-176 (Elsevier BV)

openalex publication_date 2013/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Citations

• Uniform decay estimates and the lorentz invariance of the classical wave equation
• Well-posedness for the motion of an incompressible liquid with free surface boundary
• Normal forms and quadratic nonlinear Klein‐Gordon equations
• Global solutions for the gravity water waves equation in dimension 3
• Well-posedness in Sobolev spaces of the full water wave problem in 2-D

Cited by

• Fefferman--Stein-type estimates and fractional NLS in Fourier Sobolev spaces
• Effective stability for Hamiltonian PDEs vanishing spectral gaps
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• Nondispersive solutions to the mass critical half-wave equation in two dimensions
• Dispersive estimates for time and space fractional Schrödinger equations
• Sharp Criteria of Scattering for the Fractional NLS
• Pointwise convergence along a tangential curve for the fractional Schrödinger equation
• Strichartz estimates for orthonormal families of initial data and weighted oscillatory integral estimates
• Asymptotic estimates of oscillatory integrals with general phase and singular amplitude: Applications to dispersive equations
• Gibbs measure dynamics for the fractional NLS
• Refined probabilistic global well-posedness for the weakly dispersive NLS
• Strichartz estimates for higher order Schrödinger equations with Partial regular initial data
• Global Well-posedness for the periodic fractional cubic NLS in 1D
• Global analysis of a model for capillary water waves in 2D
• Local well-posedness of semilinear space-time fractional Schrödinger equation
• Cancellations of Resonances and Long Time Dynamics of Cubic Schrödinger Equation on \mathbbT
• The cubic nonlinear fractional Schrödinger equation on the half-line
• Profile decompositions of fractional Schrödinger equations with angularly regular data
• The Nonlinear Schrodinger equation with a potential in dimension 1
• Global solutions for the gravity water waves system in 2d
• Global infinite energy solutions for the 2D gravity water waves system
• Blowup dynamics for mass critical Half-wave equation in 2D
• Modified Scattering for the Boson Star Equation
• Existence, non-existence and blow-up behavior of minimizers for the mass-critical fractional nonlinear Schrödinger equations with periodic potentials
• Two dimensional water waves in holomorphic coordinates
• The lifespan of small solutions to cubic derivative nonlinear Schrödinger equations in one space dimension
• Recent advances on the global regularity for irrotational water waves. [europepmc]