EUDML

We consider complex-valued solutions $u_{ε}$ of the Ginzburg–Landau equation on a smooth bounded simply connected domain $Ω$ of $ℝ^{N}$ , $N \geq 2$ , where $ε > 0$ is a small parameter. We assume that the Ginzburg–Landau energy $E_{ε} (u_{ε})$ verifies the bound (natural in the context) $E_{ε} (u_{ε}) \leq M_{0} | log ε |$ , where $M_{0}$ is some given constant. We also make several assumptions on the boundary data. An important step in the asymptotic analysis of $u_{ε}$ , as $ε \to 0$ , is to establish uniform $L^{p}$ bounds for the gradient, for some $p > 1$ . We review some recent techniques developed in...

Uniform estimates for the parabolic Ginzburg–Landau equation

F. Bethuel; G. Orlandi — 2010

ESAIM: Control, Optimisation and Calculus of Variations

We consider complex-valued solutions u of the Ginzburg–Landau equation on a smooth bounded simply connected domain of $ℝ^{N}$ , ≥ 2, where ε > 0 is a small parameter. We assume that the Ginzburg–Landau energy $E_{ε} (u_{ε})$ verifies the bound (natural in the context) $E_{ε} (u_{ε}) \leq M_{0} | log ε |$ , where is some given constant. We also make several assumptions on the boundary data. An important step in the asymptotic analysis of u, as ε → 0, is to establish uniform bounds for the gradient, for some . We review...

Vortex motion and phase-vortex interaction in dissipative Ginzburg-Landau dynamics

F. Bethuel; G. Orlandi; D. Smets — 2004

Journées Équations aux dérivées partielles

We discuss the asymptotics of the parabolic Ginzburg-Landau equation in dimension $N \geq 2 .$ Our only asumption on the initial datum is a natural energy bound. Compared to the case of “well-prepared” initial datum, this induces possible new energy modes which we analyze, and in particular their mutual interaction. The two dimensional case is qualitatively different and requires a separate treatment.

On the NLS dynamics for infinite energy vortex configurations on the plane.

f. bethuel; r. l. jerrard; d. smets — 2008

Revista Matemática Iberoamericana

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Énergies relaxées pour applications harmoniques

A characterization of maps in $H^{1} (B^{3}, S^{2})$ which can be approximated by smooth maps

Le problème des surfaces à courbure moyenne prescrite

Fonctionnelles de Ginzburg-Landau et espaces de configurations de particules positives et négatives

Vorticité dans les modèles de Ginzburg-Landau pour la supraconductivité

Uniform estimates for the parabolic Ginzburg–Landau equation

Uniform estimates for the parabolic Ginzburg–Landau equation

Vortex motion and phase-vortex interaction in dissipative Ginzburg-Landau dynamics

On the NLS dynamics for infinite energy vortex configurations on the plane.