Small Moving Rigid Body into a Viscous Incompressible Fluid

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• 作者：Christophe Lacave ; Takéo Takahashi
• 刊名：Archive for Rational Mechanics and Analysis
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：223
• 期：3
• 页码：1307-1335
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：Classical Mechanics; Physics, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Fluid- and Aerodynamics;
• 出版者：Springer Berlin Heidelberg
• ISSN：1432-0673
• 卷排序：223

文摘

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 \({\varepsilon}\), the energy equality is not sufficient to obtain a uniform estimate for the solid velocity. This will be achieved thanks to the optimal Lp−Lq 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 \({\mathbb{R}^{2}}\).