Properties of a single vortex solution in a rotating Bose Einstein condensate

In this Note, we study the properties of the line energy for a vortex γ in a Bose Einstein condensate rotating at velocity $\text{Ω}$. The global minimizer is either the vortex free solution or U vortices which exist only for $\text{Ω}$ bigger than a critical value. For all values of $\text{Ω}$, we prove the existence of an S type vortex, which is a critical point of the line energy, observed in the experiments. We also prove uniqueness of the minimizer for almost every $\text{Ω}$ and a monotonicity property of the curve γ with respect to $\text{Ω}$. The proofs rely on a related isoperimetric problem. To cite this article: A. Aftalion, R.L. Jerrard, C. R. Acad. Sci. Paris, Ser. I 336 (2003).