On the geometry of Gross-pitaevski vortex curves for generic data (Q2846912)

The energy integral functional NEWLINE\[NEWLINE E_0(\gamma)=\int_{a}^{b}\Big [\rho(\gamma(t))|\dot{\gamma}(t)|+B_0(\gamma(t))\dot{\gamma}(t)\Big ]dt NEWLINE\]NEWLINE arising as a \(\Gamma\)-limit of the Gross-Pitaevskii energy is considered. Here \(\gamma: (a,b)\rightarrow \Omega\) is a Lipschitz curve (a vortex), \(\rho\) is a real valued function representing a trapping potential and \(B_0\in C^{1,1}(\Omega,\mathbb{R}^3), \Omega\subset \mathbb{R}^3 \) is the region occupied by the condensate.NEWLINENEWLINEIn the present work, new properties of the functional's local minimizers are established. Moreover, a description of these minimizers is given.