Applied Maths Seminar: Bates -- Nucleation of instability of the Meissner state of 3-dimensional superconductors

This talk concerns a nonlinear partial differential system in a 3-dimensional domain
involving the operator curl^2, which is a simplified model used to examine nucleation of
instability of the Meissner state of a superconductor as the applied magnetic field
reaches the superheating field.  We derive a priori C^(2+alpha) estimates for a weak
solution H, the curl of the magnetic potential, and determine the location of the
maximal points of |curl H| which correspond to the nucleation of instability of the
Meissner state.  We show that, if the penetration length is small, the solution exhibits
a boundary layer.  If the applied magnetic field is homogeneous, |curl H| is maximal
around the points on the boundary where the applied field is tangential to the surface.  

Note: This talk is held on Monday, May 5th, 3-4pm, in Carslaw 273!