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- W2148565139 abstract "We study the Ginzburg-Landau equation on the plane with initial data being the product of n well-separated +1 vortices and spatially decaying perturbations. If the separation distances are O(ϵ−1), ϵ ≪ l, we prove that the n vortices do not move on the time scale $O(varepsilon^{-2}lambda_{varepsilon}), lambda_{varepsilon} = o(log {1over varepsilon})$; instead, they move on the time scale according to the law ẋj = − ∇xj W, W = − Σl≠j log|xl −xj|, xj = (ξj, ηj) ∈ ℝ2, the location of the jth vortex. The main ingredients of our proof consist of estimating the large space behavior of solutions, a monotonicity inequality for the energy density of solutions, and energy comparisons. Combining these, we overcome the infinite energy difficulty of the planar vortices to establish the dynamical law. © John & Wiley Sons, Inc." @default.
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- W2148565139 date "1999-10-01" @default.
- W2148565139 modified "2023-10-18" @default.
- W2148565139 title "On the dynamical law of the Ginzburg-Landau vortices on the plane" @default.
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- W2148565139 doi "https://doi.org/10.1002/(sici)1097-0312(199910)52:10<1189::aid-cpa1>3.0.co;2-t" @default.
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