Many-body blow-up profile of boson stars with external potentials

Abstract

We consider a 3D quantum system of [Formula: see text] identical bosons in a trapping potential [Formula: see text], with [Formula: see text], interacting via a Newton potential with an attractive interaction strength [Formula: see text]. For a fixed large [Formula: see text] and the coupling constant [Formula: see text] smaller than a critical value [Formula: see text] (Chandrasekhar limit mass), in an appropriate sense, the many-body system admits a ground state. We investigate the blow-up behavior of the ground state energy as well as the ground states when [Formula: see text] approaches [Formula: see text] sufficiently slowly in the limit [Formula: see text]. The blow-up profile is given by the Gagliardo–Nirenberg solutions.