Existence of 3D strong solutions for a system modeling a deformable solid inside a viscous incompressible fluid

2013/03/01 by Sébastien Court, Court, Sébastien
Mathematics · #35Q30 #74F10 #76D03 #76D05 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35Q30 #msc:74F10 #msc:76D03 #msc:76D05

paper · pdf · doi:10.48550/arxiv.1303.0163

46 pages

arxiv created 2014/07/07 · arxiv updated 2014/07/08

Abstract

In this paper we study a coupled system modeling the movement of a deformable solid immersed in a fluid. For the solid we consider a given deformation that has to obey several physical constraints. The motion of the fluid is modeled by the incompressible Navier-Stokes equations in a time-dependent bounded domain of \R³, and the solid satisfies the Newton's laws. Our contribution consists in adapting and completing some results of ARMA 2008 in dimension 3, in a framework where the regularity of the deformation of the solid is limited. We rewrite the main system in domains which do not depend on time, by using a new means of defining a change of variables, and a suitable change of unknowns. We study the corresponding linearized system before setting a local-in-time existence result. Global existence is obtained for small data, and in particular for deformations of the solid which are arbitrarily close to the identity.

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