Global solutions to the Hartree equation for large L^{p}-initial data

DOI10.1512/IUMJ.2019.68.7740zbMath1427.35256OpenAlexW2971733957MaRDI QIDQ4972825

Ryosuke Hyakuna

Publication date: 27 November 2019

Published in: Indiana University Mathematics Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1512/iumj.2019.68.7740

zbMATH Keywords

nonlinear Schrödinger equationHartree equationglobal solutions for large initial data

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) NLS equations (nonlinear Schrödinger equations) (35Q55) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Time-dependent Schrödinger equations and Dirac equations (35Q41) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (3)

On the global Cauchy problem for the Hartree equation with rapidly decaying initial data ⋮ The Hartree and Hartree-Fock equations in Lebesgue \(L^p\) and Fourier-Lebesgue \(\widehat{L}^p\) spaces ⋮ Well-posedness for the 1D cubic nonlinear Schrödinger equation in \(L^p, p > 2\)

Cites Work

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• On the global wellposedness for the nonlinear Schrödinger equations with \(L^{p}\)-large initial data
• On the global well-posedness for the nonlinear Schrödinger equations with large initial data of infinite \(L^2\) norm
• Global wellposedness for 1D nonlinear Schrödinger equation for data with an infinite \(L^2\) norm
• Analytic smoothing effect for the nonlinear Schrödinger equations without square integrability
• Trilinear \(L^p\) estimates with applications to the Cauchy problem for the Hartree-type equation
• Cauchy problem of nonlinear Schrödinger equation with initial data in Sobolev space 𝑊^{𝑠,𝑝} for 𝑝<2

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