Analysis of coupled models for fluid-structure interaction of internal flows
The modelling of the behaviour of blood flows in (large or small) arteries has to reflect two types of phenomenon that coexist: the blood flow — with any suitable model to represent its behaviour — and the artery wall displacement — with or without the tissues or muscles that surround the wall. This feature relative to the coupling of different phenomena is a new one as regards the mathematical analysis of the system of equations involved in the model and it is present independently of the complexity and the accuracy of the models chosen to represent each individual phenomenon. In addition to the theory required for analyzing each individual model, the analysis of the coupling or interaction raises new and specific difficulties. Mathematically speaking, the resulting equations are nonlinear, firstly because any realistic model for the fluid is nonlinear (cf. equation (2.1)), but also because the interaction involves a nonlinearity in addition to any anterior nonlinearity of the primitive independent model.
KeywordsBounded Sequence Stokes Problem Couple Problem Elastic Structure Transmission Problem
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