Scattering for the focusing H^1/2-critical Hartree equation with radial data

2009/06/18 by Yanfang Gao, Changxing Miao, Gao, Yanfang +3
Mathematics · Physics and Astronomy · #35Q40 #35Q55 #47J35 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Chromodynamics and Particle Interactions #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.0906.3382

openalex publication_date 2009/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the focusing H^1/2-critical nonlinear Schrödinger equation (NLS) of Hartree type i∂_t u + Δu = -(|⋅|^-3 ∗ |u|²)u with H^1/2 radial data in dimension d = 5. It is proved that if the maximal life-span solution obeys sup_t‖|∇|^1/2u‖₂ < (√(6))/(3) ‖|∇|^1/2Q‖₂, where Q is the positive radial solution to the elliptic equation(\refe14). Then the solution is global and scatters.

Citations

• Maximizers for the Strichartz inequalities and the Sobolev-Strichartz inequalities for the Schrödinger equation
• The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher

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