Size estimates of an obstacle in a stationary Stokes fluid

In this work we are interested in estimating the size of a cavity D immersed in a bounded domain Ω ⊂ ℝd = 2, 3, filled with a viscous fluid governed by the Stokes system, by means of velocity and Cauchy forces on the external boundary ∂Ω. More precisely, we establish some lower and upper bounds in terms of the difference between the external measurements when the obstacle is present and without the object. The proof of the result is based on interior regularity results and quantitative estimates of unique continuation for the solution of the Stokes system.