The defocusing \(\dot{H}^{1/2}\)-critical NLS in high dimensions

DOI10.3934/dcds.2014.34.733zbMath1295.35368arXiv1212.6816OpenAlexW2962834089MaRDI QIDQ379749

Jason Murphy

Publication date: 11 November 2013

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1212.6816

zbMATH Keywords

scatteringnonlinear Schrödinger equationglobal existenceconcentration-compactnesscritical space

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) NLS equations (nonlinear Schrödinger equations) (35Q55) Existence problems for PDEs: global existence, local existence, non-existence (35A01)

Related Items (15)

The radial mass-subcritical NLS in negative order Sobolev spaces ⋮ The defocusing energy-supercritical NLS in higher dimensions ⋮ Large data mass-subcritical NLS: critical weighted bounds imply scattering ⋮ Global well-posedness and scattering for the mass critical nonlinear Schrödinger equation with mass below the mass of the ground state ⋮ The defocusing energy-supercritical NLS in four space dimensions ⋮ Scattering and blowup beyond the mass-energy threshold for the cubic NLS with a potential ⋮ Global well-posedness for the defocusing Hartree equation with radial data in ℝ4 ⋮ Defocusing \(\dot{H}^{\frac{ 1}{ 2}} \)-critical inhomogeneous nonlinear Schrödinger equations ⋮ On the Global Well-Posedness for the Periodic Quintic Nonlinear Schrödinger Equation ⋮ Numerical simulations for the energy-supercritical nonlinear wave equation ⋮ The radial defocusing energy-supercritical NLS in dimension four ⋮ The defocusing quintic NLS in four space dimensions ⋮ 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 ⋮ The Radial Defocusing Nonlinear Schrödinger Equation in Three Space Dimensions

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