A Stability Estimate for Robin Boundary Coefficients in Stokes Fluid Flows

In this report, we examine the unsteady Stokes equations with nonhomogeneous boundary conditions. As an application of a Carleman estimate, we first establish log type stabilities for the solution of the equations from either an interior measurement of the velocity, or a boundary observation depending on the trace of the velocity and of the Cauchy stress tensor measurements on a part of the boundary. We then consider the inverse problem of determining the timeindependent Robin coefficient from a measurement of the solution and of Cauchy data on a sub-boundary.