Recovering boundary data: The Cauchy Stokes system

This paper is concerned with the severely ill-posed Cauchy–Stokes problem. We are interested in a data completion problem which is exploited to detect small leaks to control water loss Kim et al. (2008) [1]. This inverse problem is rephrased into an optimization one: An energy-like error functional is introduced. We prove that the optimality condition of the first order is equivalent to solving an interfacial equation which turns out to be a Cauchy-Steklov-Poincaré operator. Numerical trials highlight the efficiency of the method.