The vanishing limit of a rigid body in three-dimensional viscous incompressible fluid

Fuente: arXiv
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Autores principales: He, Jiao, Su, Pei
Formato: Preprint
Publicado: 2022
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author He, Jiao
Su, Pei
author_facet He, Jiao
Su, Pei
contents We consider the evolution of a small rigid body in an incompressible viscous fluid filling the whole space $\rline^3$. When the small rigid body shrinks to a "massless" point in the sense that its density is constant, we prove that the solution of the fluid-rigid body system converges to a solution of the Navier-Stokes equations in the full space. Based on some $L^p-L^q$ estimates of the fluid-structure semigroup and a fixed point argument, we obtain a uniform estimate of velocity of the rigid body. This allows us to construct admissible test functions which plays a key role in the procedure of passing to the limit.
format Preprint
id arxiv_https___arxiv_org_abs_2211_16257
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle The vanishing limit of a rigid body in three-dimensional viscous incompressible fluid
He, Jiao
Su, Pei
Analysis of PDEs
35B40, 76D05, 35Q70, 35Q35, 35Q30
We consider the evolution of a small rigid body in an incompressible viscous fluid filling the whole space $\rline^3$. When the small rigid body shrinks to a "massless" point in the sense that its density is constant, we prove that the solution of the fluid-rigid body system converges to a solution of the Navier-Stokes equations in the full space. Based on some $L^p-L^q$ estimates of the fluid-structure semigroup and a fixed point argument, we obtain a uniform estimate of velocity of the rigid body. This allows us to construct admissible test functions which plays a key role in the procedure of passing to the limit.
title The vanishing limit of a rigid body in three-dimensional viscous incompressible fluid
topic Analysis of PDEs
35B40, 76D05, 35Q70, 35Q35, 35Q30
url https://arxiv.org/abs/2211.16257