We study a variational Ginzburg–Landau-type model depending on a small parameter for (tangent) vector fields on a 2-dimensional Riemannian surface. As , the vector fields tend to be of unit length and will have singular points of a (non-zero) index, called vortices. Our main result determines the interaction energy between these vortices as a Γ-limit (at the second order) as .
Nous étudions un modèle variationnel de type Ginzburg–Landau (dépendant d'un petit paramètre ) pour des champs de vecteurs (tangents) sur une surface riemannienne. Lorsque , ces champs de vecteurs auront des points singuliers d'indice non nul, appelés tourbillons. Notre résultat détermine l'énergie d'interaction entre les tourbillons en tant que Γ-limite (au second ordre) pour .
Accepted:
Published online:
Radu Ignat 1; Robert L. Jerrard 2
@article{CRMATH_2017__355_5_515_0, author = {Radu Ignat and Robert L. Jerrard}, title = {Interaction energy between vortices of vector fields on {Riemannian} surfaces}, journal = {Comptes Rendus. Math\'ematique}, pages = {515--521}, publisher = {Elsevier}, volume = {355}, number = {5}, year = {2017}, doi = {10.1016/j.crma.2017.04.004}, language = {en}, }
Radu Ignat; Robert L. Jerrard. Interaction energy between vortices of vector fields on Riemannian surfaces. Comptes Rendus. Mathématique, Volume 355 (2017) no. 5, pp. 515-521. doi : 10.1016/j.crma.2017.04.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.04.004/
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