Blow-up of 2D attractive Bose-Einstein condensates at the critical rotational speed

Van Duong Dinh (1) , Dinh-Thi Nguyen (1) , Nicolas Rougerie (1)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

We study the ground states of a 2D focusing non-linear Schrödinger equation with rotation and harmonic trapping. When the strength of the interaction approaches a critical value from below, the system collapses to a profile obtained from the optimizer of a Gagliardo-Nirenberg interpolation inequality. This was established before in the case of fixed rotation frequency. We extend the result to rotation frequencies approaching, or even equal to, the critical frequency at which the centrifugal force compensates the trap. We prove that the blow-up scenario is to leading order unaffected by such a strong deconfinement mechanism. In particular the blow-up profile remains independent of the rotation frequency.

Mots clés: Rotational Bose-Einstein Condensate; Nonlinear Schrödinger Equation; Ground State; Blow-up

Domaines: Equations aux dérivées partielles [math.AP]

Van Duong Dinh, Dinh-Thi Nguyen, Nicolas Rougerie. Blow-up of 2D attractive Bose-Einstein condensates at the critical rotational speed. Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2023, ⟨10.4171/AIHPC/94⟩. ⟨hal-03752950v3⟩