Zhang, GuoqingSong, Ningning2021-11-292021-11-292019-05-28Zhang, G., & Song, N. (2019). Travelling solitary waves for boson stars. <i>Electronic Journal of Differential Equations, 2019</i>(73), pp. 1-12.1072-6691https://hdl.handle.net/10877/14961In this article, we study the pseudo-relativistic Hartree equation i∂tψ = (√-∆ + m2 - m)ψ - (e-μ|x| / 4π|x| ∗ |ψ|2)ψ, on ℝ3, which describes the dynamics of pseudo-relativistic boson stars with rest mass m > 0 in the mean-field limit. Based on Ekeland variational principle, concentration-compactness lemma and Gagliardo-Nirenberg inequality, we prove existence of travelling solitary waves under the critical stellar mass. In addition to their existence, we obtain orbital stability by using a general idea presented in Cazenave and Lions [2].Text12 pages1 file (.pdf)enAttribution 4.0 InternationalTravelling solitary waveBoson star equationCritical stellar massArticle