2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/120286Using variational methods, we construct approximate solutions for the Gross-Pitaevski equation which concentrate on circles in $\R^3$. These solutions will help to show that the $L^2$ flow is unstable for the usual topology and for the projective distance.15 pages, 0 figuresAnalysis of PDEs35Q55; 35B35; 81Q05text