Uniqueness of ground states for the L²-critical boson star equation

2009/05/19 by Rupert L. Frank, Enno Lenzmann, Frank, Rupert L. +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory in Mathematical Physics #math-ph #math.AP #math.MP

paper · pdf · doi:10.48550/arxiv.0905.3105

Research announcement note; submitted for publication

arxiv created 2009/05/19 · openalex publication_date 2009/05/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish uniqueness of ground states u(x) ≥ 0 for the L²-critical boson star equation √(-Δ) u - (|x|^-1 ∗ |u|²) u = -u in \R³. The proof blends variational arguments with the harmonic extension to the halfspace \R⁴₊. Apart from uniqueness, we also show radiality of ground states (up to translations) and the nondegeneracy of the linearization. Our results provide an indispensable basis for the blowup analysis of the time-dependent L²-critical boson star equation. The uniqueness proof can be generalized to different fractional Laplacians (-Δ)^s and space dimensions.

Citations

• Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation
• Nonlocal models for nonlinear, dispersive waves
• Classification of solutions for an integral equation

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