Asymptotic analysis of boosted ground states of boson stars

We investigate a minimization problem on the pseudo‐relativistic Hartree equation for boson stars, in which the energy functional is defined byE v ( ψ ) = 1 2ψ , ( − △ + m 2− m ) ψ + i 2 ⟨ ψ , ( v · ∇ ) ψ ⟩ − 1 4 ∫ R 31 | x | ∗ | ψ | 2| ψ | 2d x , where v ∈ R 3 denotes travelling velocity. Two kinds of asymptotic analysis with respect to m and the L 2 ‐norm N = ∫ R 3| ψ | 2d x will be given, respectively.