Static States for Rotating Two‐Component Bose–Einstein Condensates.

In this paper, we study static states for rotating two‐component Bose–Einstein condensates (BECs) in two and three dimensions. This leads to analyze normalized solutions for a coupled Schrödinger system with rotation. In dimension two, it corresponds to a mass‐critical problem, for which we obtain some existence and nonexistence results. In the three‐dimensional case, the problem becomes mass‐supercritical, where we prove a multiplicity result along with an accurately asymptotical analysis. Furthermore, a stability result is also established in both cases. We not only extend the main results in Ardila and Hajaiej (Journal of Dynamics and Differential Equations 35 (2023), 1643–1665), Arbunich et al. (Letters in Mathematical Physics 109 (2019), 1415–1432), and Luo and Yang (Journal of Differential Equations 304 (2021), 326–347) from the rotating one‐component BEC to rotating two‐component BECs, but we also partially extend the results of Guo et al. (Discrete and Continuous Dynamical Systems 37 (2017), 3749–3786; Journal of Differential Equations 264 (2018), 1411–1441) from nonrotating two‐component BECs to rotating two‐component BECs. [ABSTRACT FROM AUTHOR]