# American Institute of Mathematical Sciences

March  2017, 37(3): 1389-1409. doi: 10.3934/dcds.2017057

## A leading term for the velocity of stationary viscous incompressible flow around a rigid body performing a rotation and a translation

 1 Univ. Littoral Côte d'Opale, Laboratoire de mathématiques pures et appliquées Joseph Liouville, F-62228 Calais, France 2 Department of Technical Mathematics, Czech Technical University, Karlovo nám. 13, 121 35 Prague 2, Czech Republic 3 Mathematical Institute of the Academy of Sciences of the Czech Republic, Žitná 25,115 67 Prague 1, Czech Republic

* Corresponding author

Received  February 2016 Revised  October 2016 Published  December 2016

Fund Project: The Š.N. was supported by Grant Agency of the Czech Republic P201-13-00522S.

We consider the Navier-Stokes system with Oseen and rotational terms describing the stationary flow of a viscous incompressible fluid around a rigid body moving at a constant velocity and rotating at a constant angular velocity. In a previous paper, we proved a representation formula for Leray solutions of this system. Here the representation formula is used as starting point for splitting the velocity into a leading term and a remainder, and for establishing pointwise decay estimates of the remainder and its gradient.

Citation: Paul Deuring, Stanislav Kračmar, Šárka Nečasová. A leading term for the velocity of stationary viscous incompressible flow around a rigid body performing a rotation and a translation. Discrete & Continuous Dynamical Systems - A, 2017, 37 (3) : 1389-1409. doi: 10.3934/dcds.2017057
##### References:
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##### References:
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Syst., 7 (2014), 967-979.  doi: 10.3934/dcdss.2014.7.967.  Google Scholar [12] P. Deuring, S. Kračmar and Š. Nečasová, Asymptotic structure of viscous incompressible flow around a rotating body, with nonvanishing flow field at infinity, arXiv 1511.04378, to appear in ZAMP Google Scholar [13] P. Deuring, S. Kračmar, Nečasová Š and P. Wittwer, Decay estimates for linearized unsteady incompressible viscous flows around rotating and translating bodies, J. Elliptic Parabol. Equ., 1 (2015), 325-333.   Google Scholar [14] P. Deuring, S. Kračmar and S. Nečasová, Note to the problem of asymptotic behavior of viscous incompressible flow around a rotating body, Comptes Rendus Mathematique, 354 (2016), 794-798.  doi: 10.1016/j.crma.2016.05.013.  Google Scholar [15] R. Farwig, The stationary exterior 3D-problem of Oseen, Navier-Stokes equations in anisotropically weighted Sobolev spaces, Math. Z., 211 (1992), 409-447.  doi: 10.1007/BF02571437.  Google Scholar [16] R. 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