Abstract
The purpose of this work is to establish stability estimates for the unique continuation property of the nonstationary Stokes problem. These estimates hold without prescribing boundary conditions and are of logarithmic type. They are obtained thanks to Carleman estimates for parabolic and elliptic equations. Then, these estimates are applied to an inverse problem where we want to identify a Robin coefficient defined on some part of the boundary from measurements available on another part of the boundary.
Highlights
Let Ω be a regular bounded connected open set of class C2 in dimension 3
Since the work made by Fabre and Lebeau in [14], the unique continuation property of this system is a well-known property
In [22], a three-balls inequality for the stationary Stokes problem is proved which only involves the L2-norm of the velocity. It leads to a quantification of the unique continuation property like in Theorem 1 of the following type: u
Summary
Let Ω be a regular bounded connected open set of class C2 in dimension 3. In [22], a three-balls inequality for the stationary Stokes problem is proved which only involves the L2-norm of the velocity It leads to a quantification of the unique continuation property like in Theorem 1 of the following type: u. Our objective will be to identify a Robin coefficient defined on some part of the boundary from measurements available on another part of the boundary To study this inverse problem, it is capital to have an estimate of the pressure and the velocity on the whole domain like the one given by Theorem 1. We present local estimates of u and p in the interior of the domain or near the boundary We gather these inequalities to prove Theorem 1.
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