### A Stability Estimate for Robin Boundary Coefficients in Stokes Fluid Flows

*PHAN QUANG SANG, NGUYEN THUY DUNG*

#### Tóm tắt

In this report, we examine the unsteady Stokes equations with non-homogeneous 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 time-independent Robin coefficient from a measurement of the solution and of Cauchy data on a sub-boundary.

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