Non-negative global weak solutions for a degenerated parabolic system   approximating the two-phase Stokes problem
  We establish the existence of non-negative global weak solutions for a strongly couple degenerated parabolic system which was obtained as an approximation of the two-phase Stokes problem driven solely by capillary forces. Moreover, the system under consideration may be viewed as a two-phase generalization of the classical Thin Film equation. 
Joachim Escher and Bogdan-Vasile Matioc
math.AP