Analysis of the penalized 3D variable viscosity Stokes equations coupled to diffusion and transport (Q2806045)

This paper deals with the non-homogeneous Navier-Stokes system that models a coupling between a viscous fluid and a moving obstacle, and establishes the existence and uniqueness of solution to this system with regularity estimates; it is shown that the solution converges weakly to the solution of the problem in the limit of vanishing penalty parameter; also, a few numerical simulations of the flow are presented. The paper may be of interest to someone working on this topic.