Variational reduction for Ginzburg-Landau vortices
From MaRDI portal
Publication:860762
DOI10.1016/j.jfa.2006.07.006zbMath1387.35561OpenAlexW1969813414MaRDI QIDQ860762
Monica Musso, Michał Kowalczyk, Manuel A. del Pino
Publication date: 9 January 2007
Published in: Journal of Functional Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jfa.2006.07.006
Variational methods involving nonlinear operators (47J30) Singular perturbations in context of PDEs (35B25) Nonlinear elliptic equations (35J60) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Variational methods for second-order elliptic equations (35J20) Ginzburg-Landau equations (35Q56)
Related Items
Smooth branch of travelling waves for the Gross-Pitaevskii equation in R2 for small speed ⋮ Critical points via \(\Gamma \)-convergence: general theory and applications ⋮ Variational reduction for Ginzburg-Landau vortices ⋮ Renormalized energies for unit-valued harmonic maps in multiply connected domains ⋮ Vortex structures for Klein-Gordon equation with Ginzburg-Landau nonlinearity ⋮ Vortex rings for the Gross-Pitaevskii equation in \(\mathbb R^3\) ⋮ Smooth branch of rarefaction pulses for the nonlinear Schrödinger equation and the Euler-Korteweg system in 2d ⋮ A uniqueness result for the two-vortex traveling wave in the nonlinear Schrödinger equation ⋮ Entire solutions to 4 dimensional Ginzburg-Landau equations and codimension 2 minimal submanifolds ⋮ Multivortex Traveling Waves for the Gross--Pitaevskii Equation and the Adler--Moser Polynomials ⋮ Interacting helical traveling waves for the Gross-Pitaevskii equation ⋮ Some remarks concerning symmetry-breaking for the Ginzburg-Landau equation ⋮ Vortex structures for some geometric flows from pseudo-Euclidean spaces ⋮ Singular limits for the bi-Laplacian operator with exponential nonlinearity in \(\mathbb R^4\) ⋮ Critical points of the regular part of the harmonic Green function with Robin boundary condition ⋮ Traveling vortex helices for Schrödinger map equations ⋮ Asymptotic behavior of the least energy solution of a problem with competing powers ⋮ On the non-degeneracy of radial vortex solutions for a coupled Ginzburg-Landau system ⋮ Interacting helical vortex filaments in the three-dimensional Ginzburg-Landau equation ⋮ Generalized Adler--Moser Polynomials and Multiple Vortex Rings for the Gross--Pitaevskii Equation
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Vortex dynamics for the Ginzburg-Landau equation with Neumann condition
- Variational reduction for Ginzburg-Landau vortices
- Vortices in complex scalar fields
- Geometric theory of semilinear parabolic equations
- A remark on multiplicity of solutions for the Ginzburg-Landau equation
- On the asymptotic behavior of minimizers of the Ginzburg-Landau model in 2 dimensions
- Quantization effects for \(-\Delta u=u(1-| u|^ 2)\) in \(\mathbb{R}^ 2\)
- Minimax solutions of the Ginzburg-Landau equations
- Construction of singular limits for a semilinear elliptic equation in dimension 2
- Topological methods for the Ginzburg-Landau equations
- Dynamics of Ginzburg-Landau vortices
- Linear and nonlinear aspects of vortices. The Ginzburg-Landau model
- On the existence of blowing-up solutions for a mean field equation
- Local minimizers for the Ginzburg-Landau energy
- On the stability of radial solutions of the Ginzburg-Landau equation
- Solutions of Ginzburg-Landau equations and critical points of the renormalized energy
- Mixed vortex-antivortex solutions of Ginzburg-Landau equations
- On the basic concentration estimate for the Ginzburg-Landau equation
- Singular limits in Liouville-type equations
- Effective dynamics of magnetic vortices
- Stability of nonconstant steady-state solutions to a Ginzburg–Landau equation in higher space dimensions
- Shooting method for vortex solutions of a complex-valued Ginzburg–Landau equation
- Topological degree for a mean field equation on Riemann surfaces
- Gamma-convergence of gradient flows with applications to Ginzburg-Landau
- Stability in 2D Ginzburg-Landau passes to the limit
- Ginzburg-landau equation and stable steady state solutions in a non-trivial domain
- Some dynamical properties of Ginzburg-Landau vortices
- LOCAL MINIMIZERS FOR THE GINZBURG–LANDAU ENERGY NEAR CRITICAL MAGNETIC FIELD: PART I
- Ginzburg-Landau vortices
- Notes on the limit equation of vortex motion for the Ginzburg-Landau equation with Neumann condition
