4 papers
On the vortex filament conjecture for the Gross-Pitaevskii equation
Manuel del Pino, Rowan Juneman, Monica Musso +1
We establish one form of the vortex filament conjecture for the three-dimensional Gross-Pitaevskii equation. Given any smooth closed embedded binormal flow of curves on a compact t…
Vortex dynamics for the Gross-Pitaevskii equation
Manuel del Pino, Rowan Juneman, Monica Musso
We rigorously establish the formal asymptotics of Neu for Gross-Pitaevskii vortex dynamics in the plane. Given any integer , we construct a family of -vortex solutions w…
Sp(2)-invariant expanders and shrinkers in Laplacian flow
Mark Haskins, Rowan Juneman, Johannes Nordström
We show that the complete Sp(2)-invariant expanding solitons for Bryant's Laplacian flow on the anti-self-dual bundle of the 4-sphere form a 1-parameter family, and that they are a…
Solvability for the Ginzburg-Landau equation linearized at the degree-one vortex
Manuel del Pino, Rowan Juneman, Monica Musso
We consider the Ginzburg-Landau equation in the plane linearized around the standard degree-one vortex solution . Using explicit representation formulae for the Fo…