Existence of 3D Strong Solutions for a System Modeling a Deformable Solid Inside a Viscous Incompressible Fluid |
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Authors: | Sébastien Court |
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Affiliation: | 1.Laboratoire de Mathématiques UMR CNRS 6620,Université Blaise Pascal,Aubière Cedex,France |
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Abstract: | We study a coupled system modeling the movement of a deformable solid inside a viscous incompressible fluid. For the solid we consider a given deformation which 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 (mathbb {R}^3), and the solid satisfies the Newton’s laws. Our contribution consists in adapting and completing in dimension 3, some existing results, 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 close to the identity. |
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