# NOTE ON THE PROBLEM OF MOTION OF VISCOUS FLUID AROUND A ROTATING AND TRANSLATING RIGID BODY

## Authors

• Paul Deuring Université du Littoral Côte d’Opale, Centre Universitaire de la Mi-Voix 50, rue F.Buisson CS 80699, 62228 Calais Cedex, France
• Stanislav Kračmar Czech Technical University in Prague, Faculty of Mechanical Engineering, Department of Technical Mathematics, Karlovo nám. 13, 121 35 Praha 2, Czech Republic; Czech Academy of Sciences, Institute of Mathematics, Žitná 25, 11567 Praha 1, Czech Republic
• Šárka Nečasová Czech Academy of Sciences, Institute of Mathematics, Žitná 25, 11567 Praha 1, Czech Republic

## Keywords:

Incompressible fluid , rigid body, exterior domain, estimates of pressure, leading terms, artificial boundary conditions

## Abstract

We consider the linearized and nonlinear systems describing the motion of incompressible flow around a rotating and translating rigid body Ɗ in the exterior domain Ω = ℝ3 \ D , where Ɗ ⊂ ℝ3 is open and bounded, with Lipschitz boundary. We derive the L-estimates for the pressure and investigate the leading term for the velocity and its gradient. Moreover, we show that the velocity essentially behaves near the infinity as a constant times the first column of the fundamental solution of the Oseen system. Finally, we consider the Oseen problem in a bounded domain ΩR := BR ∩ Ω under certain artificial boundary conditions on the truncating boundary ∂BR, and then we compare this solution with the solution in the exterior domain Ω to get the truncation error estimate.

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2021-02-10

## Section

Non-Refereed Articles