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Uniqueness and partial identification in a geometric inverse problem for the Boussinesq system. (English) Zbl 1099.35169

Summary: We analyze the inverse problem of the identification of a rigid body immersed in a fluid governed by the stationary Boussinesq system. First, we establish a uniqueness result. Then, we present a new method for the partial identification of the body. The proofs use local Carleman estimates, differentiation with respect to domains, data assimilation techniques and controllability results for PDEs.

MSC:

35R30 Inverse problems for PDEs
35Q35 PDEs in connection with fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
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References:

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