Trilinear \(L^p\) estimates with applications to the Cauchy problem for the Hartree-type equation

DOI10.1016/j.jmaa.2018.09.014zbMath1404.35415OpenAlexW2890115650MaRDI QIDQ1798996

Gaku Hoshino, Ryosuke Hyakuna

Publication date: 18 October 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.2018.09.014

zbMATH Keywords

Cauchy problemnonlinear Schrödinger equationsHartree equation\(L^p\)-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) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (5)

Analytic smoothing effect for the nonlinear Schrödinger equations without square integrability ⋮ 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 ⋮ Global solutions to the Hartree equation for large L^{p}-initial data ⋮ Local and global well-posedness, and \(L^{p^\prime}\)-decay estimates for 1D nonlinear Schrödinger equations with Cauchy data in \(L^p\)

Cites Work

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• Short-range scattering of Hartree type fractional NLS
• Fractional Gagliardo-Nirenberg and Hardy inequalities under Lorentz norms
• Existence of solutions for Schrödinger evolution equations
• On a class of nonlinear Schrödinger equations. I. The Cauchy problem, general case
• On nonlinear Schrödinger equations. II: \(H^ S\)-solutions and unconditional well-posedness
• Short-range scattering of Hartree type fractional NLS. II.
• On the Cauchy Problem of Fractional Schrödinger Equation with Hartree Type Nonlinearity
• The Kato-Ponce Inequality
• The cauchy problem for the critical nonlinear Schrödinger equation in Hs
• Endpoint Strichartz estimates
• Cauchy problem of nonlinear Schrödinger equation with initial data in Sobolev space 𝑊^{𝑠,𝑝} for 𝑝<2
• On the Cauchy problem for the Hartree type equation in the Wiener algebra
• Pitt's inequality with sharp convolution estimates

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