TY - JOUR
T1 - Complex Ginzburg-Landau equations and dynamics of vortices, filaments, and codimension-2 submanifolds
AU - Lin, Fang Hua
PY - 1998/4
Y1 - 1998/4
N2 - Here we study the asymptotic behavior of solutions to the complex Ginzburg-Landau equations and their associated heat flows in arbitrary dimensions when the Ginzburg-Landau parameter 1/ε tends to infinity. We prove that the energies of solutions in the flow are concentrated at vortices in two dimensions, filaments in three dimensions, and codimension-2 submanifolds in higher dimensions. Moreover, we show the dynamical laws for the motion of these vortices, filaments, and codimension-2 submanifolds. Away from the energy concentration sets, we use some measure-theoretic arguments to show the strong convergence of solutions in both static and heat flow cases.
AB - Here we study the asymptotic behavior of solutions to the complex Ginzburg-Landau equations and their associated heat flows in arbitrary dimensions when the Ginzburg-Landau parameter 1/ε tends to infinity. We prove that the energies of solutions in the flow are concentrated at vortices in two dimensions, filaments in three dimensions, and codimension-2 submanifolds in higher dimensions. Moreover, we show the dynamical laws for the motion of these vortices, filaments, and codimension-2 submanifolds. Away from the energy concentration sets, we use some measure-theoretic arguments to show the strong convergence of solutions in both static and heat flow cases.
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U2 - 10.1002/(SICI)1097-0312(199804)51:4<385::AID-CPA3>3.0.CO;2-5
DO - 10.1002/(SICI)1097-0312(199804)51:4<385::AID-CPA3>3.0.CO;2-5
M3 - Article
AN - SCOPUS:0032398933
SN - 0010-3640
VL - 51
SP - 385
EP - 441
JO - Communications on Pure and Applied Mathematics
JF - Communications on Pure and Applied Mathematics
IS - 4
ER -