The focusing energy-critical Hartree equation

DOI10.1016/j.jde.2008.05.013zbMath1155.35421OpenAlexW2116721163MaRDI QIDQ2378618

Dong Li, Xiaoyi Zhang, Chang Xing Miao

Publication date: 13 January 2009

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2008.05.013

zbMATH Keywords

regularitySchrödinger equationBernstein estimatesmaximal-lifespan solution

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Almost and pseudo-almost periodic solutions to PDEs (35B15) A priori estimates in context of PDEs (35B45) NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs in connection with quantum mechanics (35Q40)

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Cites Work

• Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities
• Global well-posedness, scattering and blow-up for the energy-critical, focusing, nonlinear Schrö\-dinger equation in the radial case
• Scattering for the nonradial 3D cubic nonlinear Schrödinger equation
• Smoothing properties and retarded estimates for some dispersive evolution equations
• Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations
• The defocusing energy-critical nonlinear Schrödinger equation in higher dimensions
• A (concentration-)compact attractor for high-dimensional nonlinear Schrödinger equations
• On the blow up phenomenon of the critical nonlinear Schrödinger equation
• Global well-posedness and scattering for the higher-dimensional energy-critical nonlinear Schrö\-dinger equation for radial data
• Global Well-Posedness and Scattering for the Energy-Critical, Defocusing Hartree Equation in ℝ¹⁺ⁿ
• Minimal-mass blowup solutions of the mass-critical NLS
• Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equation in R 1+4
• Global well-posedness, scattering and blow-up for the energy-critical, focusing Hartree equation in the radial case
• Scattering for 𝐻̇^{1/2} bounded solutions to the cubic, defocusing NLS in 3 dimensions
• The focusing energy-critical nonlinear Schrödinger equation in dimensions five and higher
• Endpoint Strichartz estimates
• Global wellposedness of defocusing critical nonlinear Schrödinger equation in the radial case
• On nonlinear schrödinger equations
• Unnamed Item

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