Doubova, Anna; Fernández-Cara, Enrique; González-Burgos, Manuel; Ortega, Jaime Uniqueness and partial identification in a geometric inverse problem for the Boussinesq system. (English) Zbl 1099.35169 C. R., Math., Acad. Sci. Paris 342, No. 9, 665-670 (2006). 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. Cited in 2 Documents MSC: 35R30 Inverse problems for PDEs 35Q35 PDEs in connection with fluid mechanics 76D05 Navier-Stokes equations for incompressible viscous fluids Keywords:domain identification; stationary Boussinesq system; Carleman estimates; data assimilation; controllability PDFBibTeX XMLCite \textit{A. Doubova} et al., C. R., Math., Acad. Sci. Paris 342, No. 9, 665--670 (2006; Zbl 1099.35169) Full Text: DOI Link References: [1] C. Alvarez, C. Conca, L. Friz, O. Kavian, J.H. Ortega, An inverse problem for the Stokes system, in press; C. Alvarez, C. Conca, L. Friz, O. Kavian, J.H. Ortega, An inverse problem for the Stokes system, in press [2] Bello, J. A.; Fernández-Cara, E.; Lemoine, J.; Simon, J., The differentiability of the drag with respect to the variations of a Lipschitz domain in a Navier-Stokes flow, SIAM J. Control Optim., 35, 2, 626-640 (1997) · Zbl 0873.76019 [3] A. Doubova, E. Fernández-Cara, J.H. Ortega, A geometric inverse problem for the Navier-Stokes equation, in press; A. Doubova, E. Fernández-Cara, J.H. Ortega, A geometric inverse problem for the Navier-Stokes equation, in press · Zbl 1099.35169 [4] Fabre, C.; Lebeau, G., Prolongement unique des solutions de l’équation de Stokes, Comm. Partial Differential Equations, 21, 573-596 (1996) · Zbl 0849.35098 [5] O. Kavian, Four lectures on parameter identification in elliptic partial differential operators, Lectures at the University of Sevilla, Spain, 2002; O. Kavian, Four lectures on parameter identification in elliptic partial differential operators, Lectures at the University of Sevilla, Spain, 2002 [6] F. Murat, J. Simon, Quelques résultats sur le contrôle par un domaine géométrique, Rapport du L.A. 189, no. 74003, Université Paris VI, 1974; F. Murat, J. Simon, Quelques résultats sur le contrôle par un domaine géométrique, Rapport du L.A. 189, no. 74003, Université Paris VI, 1974 [7] Puel, J. P., A nonstandard approach to a data assimilation problem, C. R. Math. Acad. Sci. Paris, Ser. I, 335, 2, 161-166 (2002) · Zbl 1003.35042 [8] Simon, J., Differentiation with respect to the domain in boundary value problems, Numer. Funct. Anal. Optim., 2, 649-687 (1980) · Zbl 0471.35077 [9] Zuazua, E., Finite-dimensional null controllability for the semilinear heat equation, J. Math. Pures Appl. (9), 76, 3, 237-264 (1997) · Zbl 0872.93014 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.