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

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.

Note on the Problem of Motion of Viscous Fluid Around a Rotating and Translating Rigid Body

“…Comparing the coefficient γ from (1.5) in the work [21] with the coefficient β 1 from (1.9) in [24], see Theorem 4.1 below, and taking into account the boundary condition (1.7) in [21], it follows that γ and β 1 are equal.…”

“…In this section we study the asymptotic behavior of the velocity profile of the system (1.2). Let us recall known results from [26] and [24]. 9 , div u = 0 and…”

Nonlinear spectral instability of steady-state flow of a viscous liquid past a rotating obstacle

“…Finally, among the many other works studying general qualitative properties of the problem (1.1)-(1.4), we wish to mention e.g. the papers [6], [7] (by Deuring, Kračmar and Nečasová), [10] (by Farwig), [13] (by Farwig, Krbec and Nečasová), [19], [20], (by Galdi), [23] (by Galdi and Silvestre), [26] (by Geissert, Heck and Hieber), [30], [32] (by Hishida) and [33] (by Hishida and Shibata).…”