Nonlinear fractional Schrödinger equations in one dimension

2013/10/07 by Alexandru D. Ionescu, Fabio Pusateri · 13 citations
Mathematics · #Advanced Mathematical Physics Problems #Numerical methods in inverse problems #Fractional Differential Equations Solutions

paper · doi:10.1016/j.jfa.2013.08.027

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
• Blow-up criteria for fractional nonlinear Schrödinger equation
• On the global behavior of weak null quasilinear wave equations
• 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\n singular amplitude: Applications to dispersive equations
• Gibbs measure dynamics for the fractional NLS
• Strichartz estimates for higher order Schrödinger equations with Partial regular initial data
• Global Well-posedness for the periodic fractional cubic NLS in 1D