Ginzburg-Landau vortex and mean curvature flow with external force field

DOI10.1007/s10114-005-0698-yzbMath1113.35091OpenAlexW2016878323MaRDI QIDQ882758

Yan Nan Liu, Huai-Yu Jian

Publication date: 24 May 2007

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-005-0698-y

zbMATH Keywords

mean curvature flowGinzburg-Landau vortexsystem of parabolic equationsthree-dimensional superconducting thin filmstype II superconducting materials

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Degenerate parabolic equations (35K65) Nonlinear elliptic equations (35J60) Initial value problems for second-order parabolic systems (35K45)

Related Items

Evolution of hypersurfaces by the mean curvature minus an external force field, Gradient flow for the Helfrich functional, On the mean curvature flow of submanifolds in the standard Gaussian space, Skew mean curvature flow, Vortex-lines motion for the Ginzburg-Landau equation with impurity, Evolution of hypersurfaces by powers of mean curvature minus an external force field, Evolution of noncompact hypersurfaces by mean curvature minus a kind of external force field, The blow-up of the conformal mean curvature flow, Evolution of Spacelike Hypersurfaces by Mean Curvature Minus External Force Field in Minkowski Space, Spinor Ginzburg-Landau equation and mean curvature flow, The bipolar quantum drift-diffusion model, A curve flow evolved by a fourth order parabolic equation, Vortex dynamics in $\mathbb {R}^4$R4

Cites Work

• Unnamed Item
• Unnamed Item
• The vortex dynamics of a Ginzburg-Landau system under pinning effect
• Flow by mean curvature of convex surfaces into spheres
• Level set approach to mean curvature flow in arbitrary codimension
• Curvature and distance function from a manifold
• Scaling limits and regularity results for a class of Ginzburg-Landau systems
• Dynamics of Ginzburg-Landau vortices
• Asymptotic behavior of minimizers for the Ginzburg-Landau functional with weight. I
• Schrödinger flows on compact Hermitian symmetric spaces and related problems
• Heat flow for the minimal surface with Plateau boundary condition.
• Dynamics for vortices of an evolutionary Ginzburg-Landau equations in 3 dimensions.
• Long-time existence and convergence of graphic mean curvature flow in arbitrary codimension.
• Mean curvature flows of Lagrangians submanifolds with convex potentials.
• Two-dimensional graphs moving by mean curvature flow
• Singularity of mean curvature flow of Lagrangian submanifolds
• Vortex pinning by inhomogeneities in type-II superconductors.
• A model for variable thickness superconducting thin films
• Convexity and symmetry of translating solitons in mean curvature flows
• Translating solitons of mean curvature flow of noncompact spacelike hypersurfaces in Minkowski space
• Curve shortening flow in arbitrary dimensional Euclidean space
• Fundamental solution of the anisotropic porous medium equation
• Complex Ginzburg-Landau equations and dynamics of vortices, filaments, and codimension-2 submanifolds
• Computing the Ground State Solution of Bose--Einstein Condensates by a Normalized Gradient Flow
• Some dynamical properties of Ginzburg-Landau vortices
• Vortex dynamics of Ginzburg-Landau equations in inhomogeneous superconductors
• Mean curvature flow of surface in 4-manifolds