## Convergence of Meissner minimisers of the Ginzburg-Landau
energy
of superconductivity as
kappa -> infinity

### A. Bonnet, S. J. Chapman & R. Monneau

The Meissner solution of a smooth cylindrical superconducting domain
subject to
a uniform applied axial magnetic field is examined. Under an additional
convexity condition the uniqueness of the Meissner solution
is proved.
It is then shown that it is a local minimiser of
the Ginzburg-Landau energy E_kappa.
For applied fields less than a critical value
the existence of the Meissner solution is proved for
large enough Ginzburg-Landau parameter kappa.
Moreover it is proved that
the Meissner solution converges to a
local minimiser of a certain energy E_infinity in the limit
as kappa tends to infinity.
Finally, it is proved that
for kappa large enough the Meissner solution
is not a global minimiser of E_kappa.