Small moving rigid body into a viscous incompressible fluid
Résumé
We consider rigid bodies moving under the influence of a viscous fluid and we study the asymptotic as the size of the solids tends to zero. In a bounded domain, if the solids shrink to " massive " pointwise particles, we obtain a convergence to the solution of the Navier-Stokes equations independently to any possible collision of the bodies with the exterior boundary. In the case of " massless " pointwise particles, we obtain a result for a single disk moving in the full plane. In this situation, the energy equality is not sufficient, and we obtain a uniform estimate for the solid velocity thanks to the optimal L p − L q decay estimates of the Stokes semigroup.
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