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### Open Access Journals

DCDS

The article deals with the time-dependent Oseen system in
a 3D exterior domain.
It is shown that the velocity part of a weak solution to that system
decays as $\bigl(\, |x| \cdot (1+|x|-x_1) \,\bigr) ^{-1}$,
and its spatial gradient as $\bigl(\, |x| \cdot (1+|x|-x_1) \,\bigr) ^{-3/2}$, for
$|x|\to \infty $. This result is obtained for data that need not have compact support.

PROC

We consider a linearization of a model for stationary incompressible
viscous
ow past a rigid body performing a rotation and a translation.
Using a representation formula, we obtain pointwise decay bounds for the velocity
and its gradient. This result improves estimates obtained by the authors
in a previous article.

keywords:
rotating body
,
Navier-Stokes system
,
viscous incompressible
ow
,
decay
,
fundamental solution

DCDS

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.

DCDS-S

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.

DCDS-S

We consider Leray solutions of the Oseen system with rotational terms, in an exterior domain.
Such solutions are characterized by square-integrability of the gradient of the velocity
and local square-integrability of the pressure. In a previous paper, we had shown a pointwise
decay result for a slightly stronger type of solution. Here this result is extended to
Leray solutions. We thus present a second access to this result, besides the one
in G. P. Galdi, M. Kyed, Arch. Rat. Mech. Anal., 200 (2011), 21-58.

## Year of publication

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