Luc Nguyen

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math.AP2025

Mountain pass for the Ginzburg-Landau energy in a strip: solitons and solitonic vortices

Amandine Aftalion, Luc Nguyen

Motivated by recent experiments, we study critical points of the Ginzburg-Landau energy in an infinite strip where phase imprinting is applied to half of the domain. We prove that…

math.AP2025

Zero-homogeneous and $O (2)$ -equivariant critical points of the Oseen-Frank energy with multiple Frank constants

Luc Nguyen

We give an existence and classification result for zero-homogeneous and $O (2)$ -equivariant critical points of the Oseen-Frank energy with multiple Frank constants. These critical p…

math.AP2023

Minimality of vortex solutions to Ginzburg--Landau type systems for gradient fields in the unit ball in dimension $N \geq 4$

Radu Ignat, Mickael Nahon, Luc Nguyen

We prove that the degree-one vortex solution is the unique minimizer for the Ginzburg--Landau functional for gradient fields (that is, the Aviles--Giga model) in the unit ball $B^N…

Mountain pass for the Ginzburg-Landau energy in a strip: solitons and solitonic vortices

Zero-homogeneous and O(2)-equivariant critical points of the Oseen-Frank energy with multiple Frank constants

Minimality of vortex solutions to Ginzburg--Landau type systems for gradient fields in the unit ball in dimension N≥4

Zero-homogeneous and $O (2)$ -equivariant critical points of the Oseen-Frank energy with multiple Frank constants

Minimality of vortex solutions to Ginzburg--Landau type systems for gradient fields in the unit ball in dimension $N \geq 4$