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 Schr & ouml;dinger 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.