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

A representation formula for linearized stationary incompressible viscous flows around rotating and translating bodies

Pages: 237 - 253, Volume 3, Issue 2, June 2010      doi:10.3934/dcdss.2010.3.237

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Paul Deuring - Univ Lille Nord de France, 59000 Lille, 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 of the Academy of Sciences of the Czech Republic, Žitná 25, 115 67 Prague 1, Czech Republic (email)

Abstract: A Green's formula is proved for solutions of a linearized system describing the stationary flow of a viscous incompressible fluid around a rigid body which is rotating and translating. The formula in question is based on the fundamental solution obtained by integrating the time variable in the fundamental solution of the corresponding evolutionary problem.

Keywords:  viscous incompressible flow,rotating body,fundamental solution.
Mathematics Subject Classification:  35Q30, 65N30, 76D05.

Received: March 2009;      Revised: July 2009;      Available Online: April 2010.