• Corpus ID: 236924438

# Entire solutions of the magnetic Ginzburg-Landau equation in $\mathbb{R}^4$

@inproceedings{Liu2021EntireSO,
title={Entire solutions of the magnetic Ginzburg-Landau equation in \$\mathbb\{R\}^4\$},
author={Yong Liu and Xinan Ma and Juncheng Wei and Wangze Wu},
year={2021}
}
• Published 5 August 2021
• Mathematics
We construct entire solutions of the magnetic Ginzburg-Landau equations in dimension 4 using Lyapunov-Schmidt reduction. The zero set of these solutions are close to the minimal submanifolds studied by Arezzo-Pacard[1]. We also show the existence of a saddle type solution to the equations, whose zero set consists of two vertical planes in R. These two types of solutions are believed to be energy minimizers of the corresponding energy functional and lie in the same connect component of the…

## References

SHOWING 1-10 OF 28 REFERENCES

• Mathematics, Physics
• 2013
We show that there exists multi-vortex, non-radial, finite energy solutions to the magnetic Ginzburg-Landau equations on all of $${\mathbb{R}^2}$$ . We use Lyapunov-Schmidt reduction to construct
• Physics
• 2012
We consider the existence of multi-vortex solutions to the Ginzburg–Landau equations with external potential on $${\mathbb{R}^2}$$ . These equations model equilibrium states of superconductors and
Here we study the asymptotic behavior of solutions to the complex Ginzburg-Landau equations and their associated heat flows in arbitrary dimensions when the Ginzburg-Landau parameter tends to
• Mathematics
• 1999
Abstract.There is an obvious topological obstruction for a finite energy unimodular harmonic extension of a S1-valued function defined on the boundary of a bounded regular domain of Rn. When such
• Mathematics
SIAM J. Math. Anal.
• 2020
It is expected that this assumption that the corresponding Adler-Moser polynomial has no repeated root holds for any $N\in\mathbb{N}$.
• Mathematics
• 2001
Let Ω be a bounded, simply connected, regular domain of RN, N⩾2. For 0<e<1, let ue: Ω→C be a smooth solution of the Ginzburg–Landau equation in Ω with Dirichlet boundary condition ge, i.e.,[formula]
We consider local minimizers of the Ginzburg-Landau energy functional ∫1/2|∇u| 2 +1/4(1-u 2 ) 2 dx and prove that, if the 0 level set is included in a flat cylinder then, in the interior, it is
• Mathematics, Physics
• 1999
We study the linearized stability of n-vortex solutions of the magnetic Ginzburg-Landau (or Abelian-Higgs) equations. We prove that the fundamental vortices (n=1,-1) are stable for all values of the
• Physics, Mathematics
• 1994
The mathematics in this book apply directly to classical problems in superconductors, superfluids and liquid crystals. It should be of interest to mathematicians, physicists and engineers working on