Global existence and uniqueness for the magnetic Hartree equation

DOI10.1007/s00028-011-0112-4zbMath1235.35230OpenAlexW2059641450MaRDI QIDQ409220

Pei Cao

Publication date: 12 April 2012

Published in: Journal of Evolution Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00028-011-0112-4

zbMATH Keywords

uniquenessglobal existencemagnetic potential

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs in connection with quantum mechanics (35Q40) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (2)

Derivation of the Hartree equation for compound Bose gases in the mean field limit ⋮ Mean-field quantum dynamics with magnetic fields

Cites Work

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• Existence and uniqueness result for the Schrödinger-Poisson system and Hartree equation in Sobolev spaces
• Endpoint Strichartz estimates for the magnetic Schrödinger equation
• Magnetic virial identities, weak dispersion and Strichartz inequalities
• Smoothing estimates for the Schrödinger equation with unbounded potentials
• Semigroups of linear operators and applications to partial differential equations
• Strichartz and smoothing estimates for Schrödinger operators with large magnetic potentials in \(\mathbb R^3\)
• Strichartz and Smoothing Estimates for Dispersive Equations with Magnetic Potentials
• Global existence of solutions to the Cauchy problem for time-dependent Hartree equations
• Scattering Theory for the Hartree Equation
• Exact smoothing properties of Schrodinger semigroups

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