Analysis of the interaction between an incompressible fluid and a quasi-incompressible non-linear elastic structure

Fatima Abbas; Ayman Mourad

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arXiv · 1910.05195

Analysis of the interaction between an incompressible fluid and a quasi-incompressible non-linear elastic structure

Fatima Abbas·Ayman Mourad

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Abstract

We are interested in studying an unsteady fluid-structure interaction problem in a three-dimensional space. We consider a homogeneous Newtonian fluid which is modeled by the Navier-Stokes equations. Whereas the motion of the structure is described by the quasi-incompressible non-linear Saint Venant-Kirchhoff model. We establish the local in time existence and uniqueness of solution for this model. For this sake, first we rewrite the non-linearity of the elastodynamic equation in an explicit way. Then, a linearized problem is introduced in the Lagrangian reference configuration and we prove that it admits a unique solution. Based on the a priori estimates on the solution of this problem together with the fixed point theorem we prove that the non-linear problem admits a unique local in time solution. At last, by the inf-sup condition we reach to the existence of the fluid pressure.

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Fatima Abbas, Ayman Mourad. 2019-10-11. Analysis of the interaction between an incompressible fluid and a quasi-incompressible non-linear elastic structure. https://arxiv.org/abs/1910.05195

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