On the Weak Solutions to Mixed Navier-Stokes-Darcy Model
  In this paper, an a priori estimate of weak solutions to the mixed Navier-Stokes/Darcy model with Beavers-Joseph-Saffman's interface condition and the existence of a weak solution are established without the small data and/or the large viscosity restriction for the first time. Based on these results, the global uniqueness of the weak solution is obtained. 
Yanren Hou and Haibiao Zheng
math.AP math.NA