4.5 Article

Small Moving Rigid Body into a Viscous Incompressible Fluid

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ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
卷 223, 期 3, 页码 1307-1335

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SPRINGER
DOI: 10.1007/s00205-016-1058-z

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资金

  1. Agence Nationale de la Recherche, Project IFSMACS [ANR-15-CE40-0010]
  2. Agence Nationale de la Recherche, Project DYFICOLTI [ANR-13-BS01-0003-01]
  3. project Instabilities in Hydrodynamics - Paris city hall (program Emergences)
  4. Fondation Sciences Mathematiques de Paris

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We consider a single disk moving under the influence of a two dimensional 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 , 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 .

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