Existence, regularity, and asymptotic behaviour of the solutions to the Ginzburg-Landau equations on \({\mathbb{R}}^ 3\)

DOI10.1007/BF01244021zbMath0678.35086MaRDI QIDQ1124056

Yisong Yang

Publication date: 1989

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

existenceground stateGinzburg-Landau equationexternal magnetic fieldregular solutionsCoulomb gaugedecaying asymptoticsenergetically stablelowest energy level

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Applications of quantum theory to specific physical systems (81V99) Partial differential equations of mathematical physics and other areas of application (35Q99)

Related Items (11)

The existence of Ginzburg-Landau solutions on the plane by a direct variational method ⋮ Topological solutions in the self-dual Chern-Simons theory: Existence and approximation ⋮ A variational problem for a system of magnetic monopoles joined by Abrikosov vortices ⋮ Ginzburg-landau equation and stable steady state solutions in a non-trivial domain ⋮ The Meissner effect and the Ginzburg–Landau equations in the presence of an applied magnetic field ⋮ Local minimizers with vortex pinning to Ginzburg-Landau functional in three dimensions ⋮ Cauchy problem for the Ginzburg-Landau equation for the superconductivity model ⋮ Existence and asymptotic behavior of solutions to the abelian Higgs model with impurity ⋮ A non-existence result for the Ginzburg-Landau equations ⋮ An efficient iterative method for dynamical Ginzburg-Landau equations ⋮ Remarks on the existence of global minimizers for the Ginzburg-Landau energy functional

Cites Work

• On the equivalence of the first and second order equations for gauge theories
• Arbitrary N-vortex solutions to the first order Ginzburg-Landau equations
• Symmetric vortices for the Ginzberg-Landau equations of superconductivity and the nonlinear desingularization phenomenon
• On the Ginzburg-Landau equations
• On the theory of superconductivity
• On nonlinear desingularization
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