Global Well-Posedness of the Cubic Nonlinear Schrödinger Equation on Closed Manifolds

DOI10.1080/03605302.2011.642449zbMath1256.35136arXiv1008.2826OpenAlexW2021137228MaRDI QIDQ5200532

Zaher Hani

Publication date: 6 November 2012

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1008.2826

zbMATH Keywords

nonlinear Schrödinger equationglobal well-posednessStrichartz estimatesL-methodeigenfunction correlationNLS on manifolds

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) NLS equations (nonlinear Schrödinger equations) (35Q55) Partial differential equations on manifolds; differential operators (58J99) Noncompact semigroups, dispersive equations, perturbations of infinite-dimensional dissipative dynamical systems (37L50) PDEs in connection with mechanics of particles and systems of particles (35Q70)

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Global well-posedness for the cubic fractional NLS on the unit disk, Local well-posedness of the nonlinear Schrödinger equations on the sphere for data in modulation spaces, Local well-posedness of critical nonlinear Schrödinger equation on Zoll manifolds of odd-growth, Global well-posedness for the energy-critical focusing nonlinear Schrödinger equation on \(\mathbb{T}^4\), MODIFIED SCATTERING FOR THE CUBIC SCHRÖDINGER EQUATION ON PRODUCT SPACES AND APPLICATIONS, A decomposition for the Schrödinger equation with applications to bilinear and multilinear estimates, On the Global Well-Posedness for the Periodic Quintic Nonlinear Schrödinger Equation, A lower bound on the blow-up rate for the Davey-Stewartson system on the torus, Long-time instability and unbounded Sobolev orbits for some periodic nonlinear Schrödinger equations, On the high–low method for NLS on the hyperbolic space, Local and global well-posedness for a quadratic Schrödinger system on Zoll manifolds, On a priori estimates and existence of periodic solutions to the modified Benjamin-Ono equation below \(H^{1 / 2}(\mathbb{T})\), Local and global theory for the three-wave mixing Schrödinger system with quadratic interactions on Zoll manifolds, On Scattering for the Quintic Defocusing Nonlinear Schrödinger Equation on R × T²

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