Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

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

Pages: 1389 - 1409, Volume 37, Issue 3, March 2017      doi:10.3934/dcds.2017057

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

Abstract: 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.

Keywords:  Exterior domain, viscous incompressible flow, rotating body, fundamental solution, asymptotic expansion, Navier-Stokes system.
Mathematics Subject Classification:  Primary: 35Q30, 76D05; Secondary: 65N30.

Received: February 2016;      Revised: October 2016;      Available Online: December 2016.