Boson Stars with Long-range Perturbations

2019/11/01 by Wang, Qingxuan, Feng, Binhua, Li, Yuan
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1911.00389

Abstract

We consider the Boson star equation with long-range perturbation given by i∂_t ψ=√(-\triangle+m²) ψ+β((1)/(|x|^α)∗ |ψ|²)ψ-((1)/(|x|)∗ |ψ|²)ψ on ℝ³, where (1)/(|x|^α) (00 and small enough, there exists at least one maximal ground state at N=N_c. Moreover, for β>0, we find that for initial value ‖ψ₀‖²₂=N_c, the solution ψ(t) is global well-posedness, and we obtain an "orbital stability" of those maximal ground state solitary waves in some sense, which implies that such long-range perturbation pushes the Boson star system more stable. Finally, we analyse blow-up behaviours of maximal ground states when β→ 0⁺.

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