On the singular set of stationary harmonic maps.
Passage à la limite faible dans des équations aux dérivées partielles non linéaires
Vortices for a variational problem related to superconductivity
Régularité des solutions de certaines équations elliptiques en dimension deux et formule de la co-aire
Improved estimates for the Ginzburg-Landau equation : the elliptic case
We derive estimates for various quantities which are of interest in the analysis of the Ginzburg-Landau equation, and which we bound in terms of the -energy and the parameter . These estimates are local in nature, and in particular independent of any boundary condition. Most of them improve and extend earlier results on the subject.
Travelling waves for the Gross-Pitaevskii equation I
Stability in the energy space for chains of solitons of the one-dimensional Gross-Pitaevskii equation
We establish the stability in the energy space for sums of solitons of the one-dimensional Gross-Pitaevskii equation when their speeds are mutually distinct and distinct from zero, and when the solitons are initially well-separated and spatially ordered according to their speeds.
Dynamique des tourbillons de vorticité pour l’équation de Ginzburg-Landau parabolique
Motion of concentration sets in Ginzburg-Landau equations
Vortex rings for the Gross-Pitaevskii equation
We provide a mathematical proof of the existence of traveling vortex rings solutions to the Gross–Pitaevskii (GP) equation in dimension . We also extend the asymptotic analysis of the free field Ginzburg–Landau equation to a larger class of equations, including the Ginzburg–Landau equation for superconductivity as well as the traveling wave equation for GP. In particular we rigorously derive a curvature equation for the concentration set (i.e. line vortices if ).
Vortices in Ginzburg-Landau equations.
Ondes progressives pour l’équation de Gross-Pitaevskii
Cet exposé présente les résultats de l’article [] au sujet des ondes progressives pour l’équation de Gross-Pitaevskii : la construction d’une branche d’ondes progressives non constantes d’énergie finie en dimensions deux et trois par un argument variationnel de minimisation sous contraintes, ainsi que la non-existence d’ondes progressives non constantes d’énergie petite en dimension trois.
Les équations d’Euler, des ondes et de Korteweg-de Vries comme limites asymptotiques de l’équation de Gross-Pitaevskii
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