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On the existence of strong solutions to a coupled fluid-structure evolution problem. (English) Zbl 1068.35087
The work originates essentially from some problems in arteries, where fluid and structure models are coupled. Fluid flows are described by the Navier-Stokes equations (a good approximation for flows in large vessels). Concerning the structure model the so-called generalized string model is considered. The main objective is to establish a rigorous result on the existence of strong solutions to initial-boundary value problems, in which the crucial point is the study of the interaction of fluid and structure. The initial-boundary value problem is introduced, for which a previous method of the author is used, which allows a straightforward application of Schauder’s fixed point theorem to proving existence of sufficiently strong solutions to nonlinear PDE problems in reflexive Banach spaces (more generally, in duals of B-spaces).

35Q30 Navier-Stokes equations
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
46N20 Applications of functional analysis to differential and integral equations
76D05 Navier-Stokes equations for incompressible viscous fluids
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