Multilinear estimates with applications to nonlinear Schrödinger and Hartree equations in \(\widehat{L^p}\)-spaces

DOI10.1007/s00028-018-0432-8zbMath1398.35215OpenAlexW2792357645MaRDI QIDQ1991702

Ryosuke Hyakuna

Publication date: 30 October 2018

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

Full work available at URL: https://doi.org/10.1007/s00028-018-0432-8

zbMATH Keywords

Cauchy problemlocal well-posednessnonlinear Schrödinger equationsHartree equation

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items (5)

Analytic smoothing effect for the nonlinear Schrödinger equations without square integrability ⋮ Strong ill-posedness for fractional Hartree and cubic NLS equations ⋮ 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 ⋮ Norm inflation for nonlinear Schrödinger equations in Fourier-Lebesgue and modulation spaces of negative regularity

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the well-posedness of the generalized Korteweg-de Vries equation in scale-critical lr-space
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
• Inequalities for strongly singular convolution operators
• Multilinear weighted convolution of L 2 functions, and applications to nonlinear dispersive equations
• A NOTE ON THE NONLINEAR SCHRÖDINGER EQUATION IN WEAK L^pSPACES
• On existence of global solutions of Schrödinger equations with subcritical nonlinearity for $̂L^{p}$-initial data
• Inhomogeneous Strichartz estimates for the Schrödinger equation
• The cauchy problem for the critical nonlinear Schrödinger equation in Hs
• Local well-posedness for the modified KdV equation in almost critical $\widehat {H^r_s}$-spaces
• A bilinear approach to the restriction and Kakeya conjectures
• Endpoint Strichartz estimates
• INHOMOGENEOUS 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
• A restriction theorem for the Fourier transform

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