@article{55b08dd0b7624db3bf2a7f4812acb7f7,
title = "Size estimates of an obstacle in a stationary Stokes fluid",
abstract = "In this work we are interested in estimating the size of a cavity D immersed in a bounded domain Ω ⊂ ℝd = 2, 3, filled with a viscous fluid governed by the Stokes system, by means of velocity and Cauchy forces on the external boundary ∂Ω. More precisely, we establish some lower and upper bounds in terms of the difference between the external measurements when the obstacle is present and without the object. The proof of the result is based on interior regularity results and quantitative estimates of unique continuation for the solution of the Stokes system.",
keywords = "Rellich's identity, Stokes system, boundary value problems, interior regularity, inverse problems, numerical analysis, size estimate",
author = "E. Beretta and C. Cavaterra and Ortega, {J. H.} and S. Zamorano",
note = "Funding Information: This work was partially supported by PFB03-CMM and Fondecyt 1111012. The work of E Beretta was supported by GNAMPA (Gruppo Nazionale per l'Analisi Matematica, la Probabilita e le loro Applicazioni) of INdAM (Istituto Nazionale di Alta Matematica) and part of it was done while the author was visiting New York University Abu Dhabi. The work of C Cavaterra was supported by the FP7-IDEAS-ERC-StG #256872 (EntroPhase) and by GNAMPA (Gruppo Nazionale per l'Analisi Matematica, la Probabilita e le loro Applicazioni) of INdAM. Part of this work was done while J Ortega was visiting the Departamento de Matematica, Universidad Autonoma de MadridUAM and the Instituto de Ciencias Matematicas ICMATCSI, Madrid, Spain. The work of S Zamorano was supported by CONICYT-Doctorado nacional 2012-21120662, and this work was also partially supported by the Advanced Grant NUMERIWAVES/FP7-246775 of the European Research Council Executive Agency, the FA9550-15-1-0027 of AFOSR, the MTM2011-29306 and MTM2014-52347 Grants of the MINECO. Publisher Copyright: {\textcopyright} 2017 IOP Publishing Ltd.",
year = "2017",
month = feb,
doi = "10.1088/1361-6420/33/2/025008",
language = "English (US)",
volume = "33",
journal = "Inverse Problems",
issn = "0266-5611",
publisher = "IOP Publishing Ltd.",
number = "2",
}