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Hele-Shaw flow with a small obstacle

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Asymptotic analysis of the flow passing over a small obstacle in the Hele-Shaw cell is performed. The results are based on the asymptotic formulas for Green’s and Neumann functions recently obtained by Maz’ya and Movchan. Theoretical results are illustrated by the numerical simulations.

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The work has been supported by PEOPLE IAPP Project PIAP-GA-2009-251475 HYDROFRAC. This work was initiated during the visit of one of the authors, S.R., to Aberystwyth University. The support of the Royal Society by the International Travel Grant - 2010/R2 No. 45239 Travel for Collaboration is greatly acknowledged.

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Correspondence to Sergei Rogosin.

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Mishuris, G., Rogosin, S. & Wrobel, M. Hele-Shaw flow with a small obstacle. Meccanica 49, 2037–2047 (2014).

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