# American Institute of Mathematical Sciences

## Journals

DCDS
Discrete & Continuous Dynamical Systems - A 2013, 33(7): 2757-2776 doi: 10.3934/dcds.2013.33.2757
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.
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PROC
Conference Publications 2011, 2011(Special): 351-361 doi: 10.3934/proc.2011.2011.351
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.
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DCDS
Discrete & Continuous Dynamical Systems - A 2017, 37(3): 1389-1409 doi: 10.3934/dcds.2017057

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.

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DCDS-S
Discrete & Continuous Dynamical Systems - S 2010, 3(2): 237-253 doi: 10.3934/dcdss.2010.3.237
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:
DCDS-S
Discrete & Continuous Dynamical Systems - S 2014, 7(5): 967-979 doi: 10.3934/dcdss.2014.7.967
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.
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