Space-Time Fractional Nonlinear Schrödinger Equation

DOI10.1137/19M1247140zbMath1431.35173OpenAlexW2982571925MaRDI QIDQ5241106

Ricardo Grande

Publication date: 30 October 2019

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/19m1247140

zbMATH Keywords

well-posednessfractional NLSspace-time nonlocal Schrödinger equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Ill-posed problems for PDEs (35R25) NLS equations (nonlinear Schrödinger equations) (35Q55) Mittag-Leffler functions and generalizations (33E12) Fractional partial differential equations (35R11)

Related Items (13)

On a time-space fractional diffusion equation with a semilinear source of exponential type ⋮ Global well-posedness for fractional Sobolev-Galpern type equations ⋮ Global well-posedness for the cubic fractional NLS on the unit disk ⋮ Multidimensional van der Corput-type estimates involving Mittag-Leffler functions ⋮ Long time decay analysis of complex-valued fractional abstract evolution equations with delay ⋮ Global existence and convergence results for a class of nonlinear time fractional diffusion equation ⋮ Superdiffusive fractional in time Schrödinger equations: a unifying approach to superdiffusive waves ⋮ A second-order implicit difference scheme for the nonlinear time-space fractional Schrödinger equation ⋮ On nonlinear Sobolev equation with the Caputo fractional operator and exponential nonlinearity ⋮ On the existence theory of a time-space fractional Klein-Gordon-Schrödinger system ⋮ Van der Corput lemmas for Mittag-Leffler functions. II: \(\alpha\)-directions ⋮ Local well-posedness of semilinear space-time fractional Schrödinger equation ⋮ Global well-posedness and long-time behavior of the fractional NLS

Cites Work

• Unnamed Item
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• Well-posedness and ill-posedness for the cubic fractional Schrödinger equations
• A parabolic problem with a fractional time derivative
• Porous medium flow with both a fractional potential pressure and fractional time derivative
• A fractional porous medium equation
• On fractional Schrödinger equations in Sobolev spaces
• Sharp well-posedness and ill-posedness results for a quadratic nonlinear Schrödinger equation
• Space-time fractional Schrödinger equation with time-independent potentials
• Instabilities for supercritical Schrödinger equations in analytic manifolds
• The second iterate for the Navier-Stokes equation
• Loss of regularity for supercritical nonlinear Schrödinger equations
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
• The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices
• Well-posedness and ill-posedness results for the Kadomtsev-Petviashvili-I equation
• On blow-up solutions to the focusing mass-critical nonlinear fractional Schrödinger equation
• Fractional Cauchy problems on bounded domains
• Local well-posedness of semilinear space-time fractional Schrödinger equation
• A General Fractional Porous Medium Equation
• Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
• A study on blowup solutions to the focusing L2-supercritical nonlinear fractional Schrödinger equation
• Perte de régularité pour les équations d’ondes sur-critiques
• Time fractional Schrödinger equation

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