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Small moving rigid body into a viscous incompressible fluid

Abstract : We consider a single disk moving under the influence of a 2D viscous fluid and we study the asymptotic as the size of the solid tends to zero.If the density of the solid is independent of $\varepsilon$, the energy equality is not sufficient to obtain a uniform estimate for the solid velocity. This will be achieved thanks to the optimal $L^p-L^q$ decay estimates of the semigroup associated to the fluid-rigid body system and to a fixed point argument. Next, we will deduce the convergence to the solution of the Navier-Stokes equations in $\mathbb{R}^2$.
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https://hal.archives-ouvertes.fr/hal-01169436
Contributor : Christophe Lacave Connect in order to contact the contributor
Submitted on : Friday, November 4, 2016 - 1:54:56 PM
Last modification on : Saturday, October 16, 2021 - 11:18:03 AM
Long-term archiving on: : Sunday, February 5, 2017 - 1:53:01 PM

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Christophe Lacave, Takéo Takahashi. Small moving rigid body into a viscous incompressible fluid. Archive for Rational Mechanics and Analysis, Springer Verlag, 2017, 223 (3), pp.1307--1335. ⟨10.1007/s00205-016-1058-z⟩. ⟨hal-01169436v2⟩

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