The defocusing energy-critical nonlinear Schrödinger equation in higher dimensions

2005/08/16 by Monica Vişan, Visan, Monica · 13 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.math/0508298

openalex publication_date 2005/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain global well-posedness, scattering, and global L^{(2(n+2))/(n-2)}_t,x spacetime bounds for energy-space solutions to the energy-critical nonlinear Schrödinger equation in \R_t× \Rⁿ_x, n≥ 5.

Cited by

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• Scattering for the 2d NLS with inhomogeneous nonlinearities
• Regularization for the Schrödinger equation with rough potential: high-dimensional case
• Regularization for the Schrödinger equation with rough potential: one-dimensional case
• Finite-mass soliton-type rigidity and four-channel reduction for the three-dimensional nonradial focusing energy-critical nonlinear Schrödinger equation
• Nonlinear Schrödinger equation with Ornstein-Uhlenbeck operator
• Sharp bilinear eigenfunction estimate, L^∞_x2L^p_t,x1-type Strichartz estimate, and energy-critical NLS
• Well-posedness and scattering of odd solutions for the defocusing INLS in one dimension
• Dynamics of subcritical threshold solutions for the 4d energy-critical NLS
• Asymptotic behavior of mass-critical Schrödinger equation in ℝ
• Global well-posedness for the defocusing, quintic nonlinear Schrödinger equation in one dimension
• Refined Scattering and Hermitian Spectral Theory for Linear Higher-Order Schrödinger Equations
• Critical scattering for the nonlinear Schrödinger equation on waveguide manifolds

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