engleski

Existence and regularity for weak solutions for a fluid interacting with a non-linear shell in 3D

We study the unsteady incompressible Navier Stokes equations in three dimensions interacting with a non-linear flexible shell of Koiter Type. The latter one constitutes a moving part of the boundary of the physical domain of the fluid. This leads to a coupled system of non-linear PDEs where the moving part of the boundary is an unknown of the problem. We study weak solutions to the corresponding fluid-structure interaction (FSI) problem. The known existence theory for weak solutions is extended to non-linear Koiter shell models. This is achieved by introducing new methods that allow us to prove higher regularity estimates for the shell by transferring damping effects from the fluid dissipation. The regularity result depends on the geometric constitution alone and is independent of the approximation procedure ; hence it holds for arbitrary weak solutions.

Fluid-structure interaction ; weak solution ; Koiter shell

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