DE Seminar: Boris Muha
University of Zagreb
Location
Mathematics/Psychology : 401
Date & Time
April 17, 2023, 11:00 am – 12:00 pm
Description
Title: Existence and regularity of weak solutions for a
fluid interacting with a non-linear shell in three
dimensions
Speaker: Boris Muha
Department of Mathematics, Faculty of Science University of Zagreb, Bijenicka 30, Zagreb,
Croatia borism@math.hr
Abstract: We study the unsteady incompressible Navier-Stokes equations in three
dimensions interacting with a non-linear flexible shell of Koiter type. This
leads to a coupled system of non-linear PDEs where the moving part of the
boundary is an unknown of the problem. The known existence theory for
weak solutions is extended to non-linear Koiter shell models. We introduce
a-priori estimates that reveal higher regularity of the shell displacement
beyond energy estimates. These are essential for non-linear Koiter shell
models, since such shell models are non-convex (w.r.t. terms of highest
order). The estimates are obtained by introducing new analytical tools
that allow to exploit dissipative effects of the fluid for the (non-dissipative)
solid. The regularity result depends on the geometric constitution alone
and is independent of the approximation procedure; hence it holds for
arbitrary weak solutions. The developed tools are further used to introduce a generalized Aubin-Lions type compactness result suitable for
fluid-structure interactions. This is a joint work with S. Schwarzacher.
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