Data completion for the Stokes system

This Note is concerned with the severely ill-posed Cauchy–Stokes problem. 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 present method. To cite this article: A. Ben Abda et al., C. R. Mecanique 337 (2009).