A Source Reconstruction Algorithm for the Stokes System from Incomplete Velocity Measurements

We consider the inverse problem of determining the spatial dependence of a source of the form f (x)ω(t) in the Stokes system defined in ω × (0, T), assuming that ω(t) is known and f (x) is divergence-free. The only available observation is a single internal measurement of the velocity and the acceleration, for which one of its components is missing. Under adequate hypothesis on ω we prove uniqueness of this inverse problem and we establish an explicit reconstruction formula. This formula provides the spectral coefficients fk of the source f in terms of a family of null controls h(ω) for the corresponding adjoint system indexed by T (0, T]. © 2017 IOP Publishing Ltd.