Navier-Stokes-Oseen flows in the exterior of a rotating and translating obstacle

Trinh Viet Duoc

doi:10.3934/dcds.2018145

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2018, Volume 38, Issue 7: 3387-3405. Doi: 10.3934/dcds.2018145

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Navier-Stokes-Oseen flows in the exterior of a rotating and translating obstacle

Trinh Viet Duoc^,

Vietnam National University, Hanoi University of Science, Faculty of Mathematics, Mechanics, and Informatics, 334 Nguyen Trai, Hanoi, Vietnam

* Corresponding author: Trinh Viet Duoc
* Corresponding author: Trinh Viet Duoc

Received: June 30, 2017

Revised: December 31, 2017

Published: June 2018

This research is funded by the Vietnam National University, Hanoi (VNU) under project number QG.17.07.

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Abstract

In this paper, we investigate Navier-Stokes-Oseen equation describing flows of incompressible viscous fluid passing a translating and rotating obstacle. The existence, uniqueness, and polynomial stability of bounded and almost periodic weak mild solutions to Navier-Stokes-Oseen equation in the solenoidal Lorentz space $ L^{3}_{σ, w} $ are shown. Moreover, we also prove the unique existence of time-local mild solutions to this equation in the solenoidal Lorentz spaces $ L^{3,q}_{σ} $.

Keywords:

Bounded and almost periodic weak mild solutions,
time-local mild solutions,
Navier-Stokes-Oseen equation,
Navier-Stokes equation,
Oseen operator,
rotating and translating obstacle.

Mathematics Subject Classification: Primary: 35B15, 35B35, 35Q30; Secondary: 76D07.

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