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

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.