A note on the fractional Schrödinger equation of Choquard type

DOI10.1016/j.jmaa.2018.10.045zbMath1412.35372OpenAlexW2897658284MaRDI QIDQ1630616

Tarek Saanouni

Publication date: 10 December 2018

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2018.10.045

zbMATH Keywords

blow-upglobal existenceGagliardo-Nirenberg inequalitynonlinear fractional Schrödinger-Choquard equation

Mathematics Subject Classification ID

Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Blow-up in context of PDEs (35B44) Fractional partial differential equations (35R11)

Related Items (21)

Well-Posedness and Blow-Up for the Fractional Schrödinger- Choquard Equation ⋮ Symmetry of positive solutions to Choquard type equations involving the fractional \(p\)-Laplacian ⋮ Fractional Choquard equations with an inhomogeneous combined non-linearity ⋮ Decay of radial solutions to a class of defocusing mass-sub-critical fractional Schrödinger equations ⋮ On blowup solutions for the mixed fractional Schrödinger equation of Choquard type ⋮ Non-linear bi-harmonic Choquard equations ⋮ Well-posedness and blow-up of Virial type for some fractional inhomogeneous Choquard equations ⋮ The radial bi-harmonic generalized Hartree equation revisited ⋮ Sharp weighted Strichartz estimates and critical inhomogeneous Hartree equations ⋮ Blow-up criteria and instability of normalized standing waves for the fractional Schrödinger-Choquard equation ⋮ Scattering theory for a class of radial focusing inhomogeneous Hartree equations ⋮ Existence of stable standing waves for the fractional Schrödinger equations with combined power-type and Choquard-type nonlinearities ⋮ Potential well theory for the focusing fractional Choquard equation ⋮ A note on Choquard equations in two space dimensions ⋮ Scattering theory for a class of defocusing energy-critical Choquard equations ⋮ Energy scattering for the focusing fractional generalized Hartree equation ⋮ Sharp threshold of global well-posedness vs finite time blow-up for a class of inhomogeneous Choquard equations ⋮ Scattering for a radial defocusing inhomogeneous Choquard equation ⋮ The generalized Hartree equation with a combined source term ⋮ Sharp thresholds of blow-up and global existence for the Schrödinger equation with combined power-type and Choquard-type nonlinearities ⋮ Scattering for radial defocusing inhomogeneous bi-harmonic Schrödinger equations

Cites Work

• Unnamed Item
• Unnamed Item
• On the Cauchy problem for the Schrödinger-Hartree equation
• Blowup for fractional NLS
• Soliton and blow-up solutions to the time-dependent Schrödinger-Hartree equation
• Soliton dynamics for the generalized Choquard equation
• Strong instability of standing waves for a nonlocal Schrödinger equation
• Well-posedness for semi-relativistic Hartree equations of critical type
• Symétrie et compacité dans les espaces de Sobolev
• Dispersion of small amplitude solutions of the generalized Korteweg-de Vries equation
• On blow-up solutions to the focusing mass-critical nonlinear fractional Schrödinger equation
• Improved Strichartz estimates for a class of dispersive equations in the radial case and their applications to nonlinear Schrödinger and wave equations
• Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics
• Derivation of Pekar's Polarons from a Microscopic Model of Quantum Crystal
• On the Cauchy Problem of Fractional Schrödinger Equation with Hartree Type Nonlinearity
• Mean field dynamics of boson stars
• A Note on Berestycki-Cazenave's Classical Instability Result for Nonlinear Schrödinger Equations
• The Choquard equation and related questions
• On fractional Choquard equations
• SOBOLEV INEQUALITIES WITH SYMMETRY
• On finite time blow-up for the mass-critical Hartree equations

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