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Dinh-Thi, Nguyen (2019): Many-body blow-up profile of boson stars with external potentials. In: Reviews in Mathematical Physics, Vol. 31, No. 10, 1950034
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We consider a 3D quantum system of N identical bosons in a trapping potential vertical bar x vertical bar(p), with p >= 0, interacting via a Newton potential with an attractive interaction strength a(N). For a fixed large N and the coupling constant a(N) smaller than a critical value a(*) (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 a(N) approaches a(*) sufficiently slowly in the limit N -> infinity. The blow-up profile is given by the Gagliardo-Nirenberg solutions.