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On the slow motion of vortices in the Ginzburg-Landau heat flow. (English) Zbl 0838.35102

Summary: We study vortex motion in the Ginzburg-Landau flow. We consider this flow in the limit of large Ginzburg-Landau parameter. It is shown that when this parameter tends to infinity, the vortex mobility tends to zero. Our proof is based on an a priori estimate on the growth of a new weighted energy and on the recent work of Bethuel, Brezis, and Helein on \(S^1\)-valued harmonic mappings in \(\mathbb{R}^2\).

MSC:

35Q35 PDEs in connection with fluid mechanics
76B47 Vortex flows for incompressible inviscid fluids
82D55 Statistical mechanics of superconductors
82D30 Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses)
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