On the Velocity of a Small Rigid Body in a Viscous Incompressible Fluid in Dimension Two and Three

In this paper we study the evolution of a small rigid body in a viscous incompressible fluid, in particular we show that a small particle is not accelerated by the fluid in the limit when its size converges to zero under a lower bound on its mass. This result is based on a new a priori estimate on t...

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Bibliographic Details
Published in:Journal of dynamics and differential equations 2024-12, Vol.36 (4), p.3109-3124
Main Authors: Bravin, Marco, Nečasová, Šárka
Format: Article
Language:English
Subjects:
Applications of Mathematics
Fluid flow
Incompressible flow
Incompressible fluids
Lower bounds
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Rigid structures
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Summary:In this paper we study the evolution of a small rigid body in a viscous incompressible fluid, in particular we show that a small particle is not accelerated by the fluid in the limit when its size converges to zero under a lower bound on its mass. This result is based on a new a priori estimate on the velocities of the centers of mass of rigid bodies that holds in the case when their masses are also allowed to decrease to zero.
ISSN:1040-7294
1572-9222
DOI:10.1007/s10884-023-10263-5