Abstract
We study steady flow of a second grade fluid past an obstacle in three space dimensions. We prove existence of solution in weighted Lebesgue spaces with anisotropic weights and thus existence of the wake region behind the obstacle. We use properties of the fundamental Oseen tensor together with results achieved in Koch (Quad Mat 15:59–122, 2004) and properties of solutions to steady transport equation to get up to arbitrarily small ε the same decay as the Oseen fundamental solution.
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Communicated by I. Straskraba
The work of the first author was partially supported by Polish grant No. N N201 547 438.
The second author was supported by the project LC06052 (Jindřich Nečas Center for Mathematical Modeling), by the Charles University Grant Agency under Contract 2509/2007 and by the Grant Agency of the Czech Republic (number GA201/08/0315). Current affiliation of the second author is Institute of Mathematics, Academy of Sciences of the Czech Republic, email: kreml@math.cas.cz.
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Konieczny, P., Kreml, O. On the 3D Steady Flow of a Second Grade Fluid Past an Obstacle. J. Math. Fluid Mech. 14, 295–309 (2012). https://doi.org/10.1007/s00021-011-0057-y
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DOI: https://doi.org/10.1007/s00021-011-0057-y