Stability estimates for the unique continuation property of the Stokes system and for an inverse boundary coefficient problem

In the first part of this paper, we prove H¨ older and logarithmic stability estimates associated with the unique continuation property for the Stokes system. The proof of these results is based on local Carleman inequalities. In the second part, these estimates on the fluid velocity and on the fluid pressure are applied to solve an inverse problem: we consider the Stokes system completed with mixed Neumann and Robin boundary conditions, and we want to recover the Robin coefficient (and obtain the stability estimate for it) from measurements available on a part of the boundary where the Neumann conditions are prescribed. For this identification parameter problem, we obtain a logarithmic stability estimate under the assumption that the velocity of a given reference solution stays far from zero on a part of the boundary where the Robin conditions are prescribed.