Failure of hydrodynamics within the vortex liquid phase
  The recent discovery that some of the coefficients of the viscosity tensor are negative is shown to invalidate the hydrodynamic approach to the vortex liquid phase of a type-II superconductor. A satisfactory theory requires retention of all the spatial gradients of the velocities or electric fields and not just the first derivatives, as assumed in a hydrodynamic theory. We illustrate such a procedure by using time-dependent Ginzburg-Landau theory to determine the electric field distribution near a single ``twin-plane boundary" due to a current passing through the boundary. 
T. Blum and M.A. Moore