Improved Interaction Morawetz Inequalities for the Cubic Nonlinear Schrödinger Equation on ℝ2

DOI10.1093/imrn/rnm090zbMath1142.35085arXivmath/0703606OpenAlexW1982235828MaRDI QIDQ5439956

James E. Colliander, Nikolaos Tzirakis, Manoussos G. Grillakis

Publication date: 30 January 2008

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0703606

zbMATH Keywords

nonlinear Schrödinger equationStrichartz estimateglobal well-posednessinteraction Morawetz inequalityMorawetz estimate

Mathematics Subject Classification ID

Related Items (13)

Quadratic Morawetz inequalities and asymptotic completeness in the energy space for nonlinear Schrödinger and Hartree equations ⋮ Global well-posedness for a \(L^2\)-critical nonlinear higher-order Schrödinger equation ⋮ Decay in energy space for the solution of fourth-order Hartree-Fock equations with general non-local interactions ⋮ Global analysis for rough solutions to the Davey-Stewartson system ⋮ Global well-posedness for the defocusing Hartree equation with radial data in ℝ4 ⋮ On the Global Well-Posedness for the Periodic Quintic Nonlinear Schrödinger Equation ⋮ Global well-posedness and scattering for the defocusing \(H^{\frac 1 2}\)-subcritical Hartree equation in \(\mathbb R^d\) ⋮ Tensor products and correlation estimates with applications to nonlinear Schrödinger equations ⋮ Global well-posedness and scattering for the defocusing \(\dot{H}^{1/2}\)-critical nonlinear Schrödinger equation in \(\mathbb{R}^2\) ⋮ On scattering for the defocusing high dimensional inter-critical NLS ⋮ Dispersion dynamics for the defocusing generalized Korteweg-de Vries equation ⋮ The cubic nonlinear Schrödinger equation in two dimensions with radial data ⋮ Global well-posedness and scattering for the defocusing, $L^{2}$-critical nonlinear Schrödinger equation when $d ≥3$

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