Global well-posedness of the magnetic Hartree equation with non-Strichartz external fields

DOI10.1088/0951-7715/28/8/2743zbMath1330.35408OpenAlexW2215913569MaRDI QIDQ3196540

Alessandro Michelangeli

Publication date: 29 October 2015

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0951-7715/28/8/2743

zbMATH Keywords

quadratic formsenergy methodsself-adjointnessnon-linear Schrödinger equationHartree equationmagnetic Strichartz estimates

Mathematics Subject Classification ID

A priori estimates in context of PDEs (35B45) NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs in connection with quantum mechanics (35Q40) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Initial value problems for nonlinear higher-order PDEs (35G25) General (adjoints, conjugates, products, inverses, domains, ranges, etc.) (47A05) Forms (bilinear, sesquilinear, multilinear) (47A07)

Related Items (5)

Global well-posedness for the non-linear Maxwell-Schrödinger system ⋮ Global, finite energy, weak solutions for the NLS with rough, time-dependent magnetic potentials ⋮ Intertwining solutions for magnetic relativistic Hartree type equations ⋮ Derivation of the Hartree equation for compound Bose gases in the mean field limit ⋮ On the mean-field approximation of many-boson dynamics

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