TY - JOUR
T1 - A product estimate for Ginzburg-Landau and application to the gradient-flow
AU - Sandier, Etienne
AU - Serfaty, Sylvia
PY - 2003/6/15
Y1 - 2003/6/15
N2 - 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.
AB - 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.
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U2 - 10.1016/S1631-073X(03)00224-3
DO - 10.1016/S1631-073X(03)00224-3
M3 - Article
AN - SCOPUS:0042205130
SN - 1631-073X
VL - 336
SP - 997
EP - 1002
JO - Comptes Rendus Mathematique
JF - Comptes Rendus Mathematique
IS - 12
ER -