The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher

2007/08/06 by Rowan Killip, Monica Vişan, Killip, Rowan +3 · 13 citations
Mathematics · Physics and Astronomy · #35Q55 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.0708.0849

openalex publication_date 2007/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish global well-posedness and scattering for solutions to the mass-critical nonlinear Schrödinger equation iu_t + Δu = ± |u|^4/d u for large spherically symmetric L²_x(R^d) initial data in dimensions d≥ 3. In the focusing case we require that the mass is strictly less than that of the ground state. As a consequence, we obtain that in the focusing case, any spherically symmetric blowup solution must concentrate at least the mass of the ground state at the blowup time.

Citations

• Uniqueness of positive solutions of Δu−u+up=0 in Rn

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