On the solvability of models for two-phase flows of viscous incompressible fluid with shear-dependent viscosity
In this paper we consider a model describing the motion of a mixture of two incompressible and (partially) immiscible fluids in d d -dimension (d?4 d ? 4 ) space domain whose viscosities have a p p -structure depending on the shear rate (or called with shear-dependent viscosity). The existence of weak solutions is established for the exponent p ? p 1 ? d + 3 d 2 + 4 d d + 2 under the no-slip boundary condition to velocity and non-flux boundary condition to relative density. This improves the known results proved for p ? 3 d + 2 d + 2 in Kim etal. (2006).
shear-dependent viscosity existence weak solution incompressible viscous fluid