Collisions and phase-vortex interactions in dissipative Ginzburg-Landau dynamics

DOI10.1215/S0012-7094-05-13034-4zbMath1087.35008OpenAlexW2063067341MaRDI QIDQ812555

Didier Smets, Giandomenico Orlandi, Fabrice Bethuel

Publication date: 24 January 2006

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-05-13034-4

zbMATH Keywords

two space dimensionsdifferent time scalesmultiple-scale expansionvortex annihilationvortex drift

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Singular perturbations in context of PDEs (35B25) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05)

Related Items (17)

Unnamed Item ⋮ Structural descriptions of limits of the parabolic Ginzburg-Landau equation on closed manifolds ⋮ Dynamics of Ginzburg-Landau and Gross-Pitaevskii vortices on manifolds ⋮ Slow motion for gradient systems with equal depth multiple-well potentials ⋮ Properties of Screw Dislocation Dynamics: Time Estimates on Boundary and Interior Collisions ⋮ Mean field limits of the Gross-Pitaevskii and parabolic Ginzburg-Landau equations ⋮ Vortex dynamics in the presence of excess energy for the Landau-Lifshitz-Gilbert equation ⋮ Vortex collisions and energy-dissipation rates in the Ginzburg-Landau heat flow ⋮ Mean field limits for Ginzburg-Landau vortices ⋮ Limiting motion for the parabolic Ginzburg-Landau equation with infinite energy data ⋮ Ginzburg-Landau vortex dynamics driven by an applied boundary current ⋮ Refined Jacobian estimates and Gross-Pitaevsky vortex dynamics ⋮ GINZBURG–LANDAU VORTEX LINES AND THE ELASTICA FUNCTIONAL ⋮ Metastability and dynamics of discrete topological singularities in two dimensions: a \(\Gamma\)-convergence approach ⋮ Dynamics of multiple degree Ginzburg-Landau vortices ⋮ Numerical Study of Quantized Vortex Interactions in the Nonlinear Schrödinger Equation on Bounded Domains ⋮ VORTEX LIQUIDS AND THE GINZBURG–LANDAU EQUATION

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