On the Cauchy problem for the Hartree type equation in the Wiener algebra

DOI10.1090/S0002-9939-2014-12072-7zbMath1293.35288arXiv1205.3615OpenAlexW3122784209MaRDI QIDQ5418556

Lounès Mouzaoui, Rémi Carles

Publication date: 4 June 2014

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1205.3615

zbMATH Keywords

well-posednessWiener algebraHartree equation

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) A priori estimates in context of PDEs (35B45) NLS equations (nonlinear Schrödinger equations) (35Q55) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Existence problems for PDEs: global existence, local existence, non-existence (35A01)

Related Items (13)

Analytic smoothing effect for the nonlinear Schrödinger equations without square integrability ⋮ Modulation spaces and non-linear Hartree type equations ⋮ The Wigner-Poisson-\(X_\alpha\) system in Wiener algebra ⋮ 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 Cauchy problem for the Hartree type equation in modulation spaces ⋮ The Hartree and Hartree-Fock equations in Lebesgue \(L^p\) and Fourier-Lebesgue \(\widehat{L}^p\) spaces ⋮ Multilinear estimates with applications to nonlinear Schrödinger and Hartree equations in \(\widehat{L^p}\)-spaces ⋮ The Cauchy problem for non-linear higher order Hartree type equation in modulation spaces ⋮ Trilinear \(L^p\) estimates with applications to the Cauchy problem for the Hartree-type equation ⋮ Local and global well-posedness, and \(L^{p^\prime}\)-decay estimates for 1D nonlinear Schrödinger equations with Cauchy data in \(L^p\) ⋮ On the existence of global solutions of the Hartree equation for initial data in the modulation space \(M^{p , q}(\mathbb{R})\) ⋮ Global well-posedness for fractional Hartree equation on modulation spaces and Fourier algebra

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