Well-posedness for a mean field model of Ginzburg-Landau vortices with opposite degrees

DOI10.1007/s00030-011-0121-6zbMath1251.35157OpenAlexW2054257923MaRDI QIDQ430758

Edoardo Mainini

Publication date: 26 June 2012

Published in: NoDEA. Nonlinear Differential Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00030-011-0121-6

zbMATH Keywords

hydrodynamic equationssuperconductivityoptimal transportationWasserstein distancevortex degreevortex density

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) PDEs in connection with fluid mechanics (35Q35) Dynamics induced by flows and semiflows (37C10) Ginzburg-Landau equations (35Q56)

Related Items

Convergence of Regularized Nonlocal Interaction Energies ⋮ Many-particle limit for a system of interaction equations driven by Newtonian potentials ⋮ Uniqueness for Keller-Segel-type chemotaxis models ⋮ Global solutions of aggregation equations and other flows with random diffusion ⋮ A description of transport cost for signed measures ⋮ Convergence and non-convergence of many-particle evolutions with multiple signs ⋮ Atomistic origins of continuum dislocation dynamics

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Gradient flow of the Chapman-Rubinstein-Schatzman model for signed vortices
• Uniqueness of the solution to the Vlasov--Poisson system with bounded density
• Ordinary differential equations, transport theory and Sobolev spaces
• Dynamics of vortices in Ginzburg-Landau theories with applications to superconductivity
• A convexity principle for interacting gases
• Dynamics of labyrinthine pattern formation in magnetic fluids: A mean-field theory
• On the hydrodynamic limit of Ginzburg-Landau vortices.
• Elliptic partial differential equations of second order
• Global solutions to vortex density equations arising from sup-conductivity
• On a model of rotating superfluids
• Numerical analysis of a mean field model of superconducting vortices
• Vorticity and Incompressible Flow
• A rigorous derivation of a free-boundary problem arising in superconductivity
• A gradient flow approach to an evolution problem arising in superconductivity
• Polar factorization and monotone rearrangement of vector‐valued functions
• The Variational Formulation of the Fokker--Planck Equation
• Existence of Weak Solutions to Some Vortex Density Models
• Analysis of a mean field model of superconducting vortices
• A Mean-Field Model of Superconducting Vortices in Three Dimensions
• A mean-field model of superconducting vortices
• Optimal Transport