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Complex Ginzburg-Landau equations and dynamics of vortices, filaments, and codimension-2 submanifolds

✍ Scribed by Fang Hua Lin

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
386 KB
Volume
51
Category
Article
ISSN
0010-3640

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✦ Synopsis

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.

📜 SIMILAR VOLUMES

On the global existence and small disper
On the global existence and small dispersion limit for a class of complex Ginzburg–Landau equations
✍ Hongjun Gao; Xueqin Wang 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 150 KB 👁 1 views

## Abstract In this paper we consider a class of complex Ginzburg–Landau equations. We obtain sufficient conditions for the existence and uniqueness of global solutions for the initial‐value problem in __d__‐dimensional torus 𝕋^__d__^, and that solutions are initially approximated by solutions of t