##
**Complex Ginzburg-Landau equations and dynamics of vortices, filaments, and codimension-2 submanifolds.**
*(English)*
Zbl 0932.35121

The paper deals with the asymptotic analysis of solutions to the complex Ginzburg-Landau system and the study of the associated heat flows in arbitrary dimensions. One of the goals of this work is to 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). A second purpose of the paper is the study of the dynamical laws for the motion of these vortices, filaments, and codimension-2 submanifolds. Finally, the author establishes a strong convergence result for solutions of complex Ginzburg-Landau equations and their associated heat flows.

The paper is a significant contribution in the mathematical study of dynamical laws associated to the Ginzburg-Landau equation occuring in superconductivity.

The paper is a significant contribution in the mathematical study of dynamical laws associated to the Ginzburg-Landau equation occuring in superconductivity.

Reviewer: Vicentiu D.Rădulescu (Craiova)

### MSC:

35K60 | Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations |

35A20 | Analyticity in context of PDEs |

49Q20 | Variational problems in a geometric measure-theoretic setting |

82D55 | Statistical mechanics of superconductors |

35B40 | Asymptotic behavior of solutions to PDEs |