This paper concerns mathematical theory of Meissner states of a bulk superconductor of type II, which occupies a bounded domain Ω in R 3 and is subjected to an applied magnetic field below the critical field HS. A Meissner state is described by a solution (f, A) of a nonlinear partial differential system called Meissner system, where f is a positive function on Ω which is equal to the modulus of the order parameter, and A is the magnetic potential defined on the entire space such that the inner trace of the normal component on the domain boundary ∂Ω vanishes. Such a solution is called a Meissner solution. Various properties of the Meissner solutions are examined, including regularity, classification and asymptotic behavior for large value of the Ginzburg-Landau parameter κ. It is shown that the Meissner solution is smooth in Ω, however the regularity of the magnetic potential outside Ω can be rather poor. This observation leads to the ides of decomposition of the Meissner system into two problems, a boundary value problem in Ω and an exterior problem outside of Ω. We show that the solutions of the boundary value problem with fixed boundary data converges uniformly on Ω as κ tends to ∞, where the limit field of the magnetic potential is a solution of a nonlinear curl system. This indicates that, the magnetic potential part A of the solution (f, A) of the Meissner system, which has same tangential component of curl A on ∂Ω, converges to a solution of the curl system as κ increases to infinity, which verifies that the curl system is indeed the correct limit of the Meissner system in the case of three dimensions.Published in: