We prove a new inequality for the Jacobian (or vorticity) associated to the Ginzburg-Landau energy in any dimension, and give static and dynamical corollaries. We then present a method to prove convergence of gradient-flows of families of energies which Gamma-converge to a limiting energy, which we apply to establish, thanks to the previous dynamical estimate, the limiting dynamical law of a finite number of vortices for the heat-flow of Ginzburg-Landau in dimension 2, with and without magnetic field.
|Translated title of the contribution||A product estimate for Ginzburg-Landau and application to the gradient-flow|
|Number of pages||6|
|Journal||Comptes Rendus Mathematique|
|State||Published - Jun 15 2003|
ASJC Scopus subject areas