1Department of Mathematical Analysis and Numerical Mathematics, Faculty od Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovakia 2Faculty of Natural Sciences II, Institute of Mathematics, Martin-Luther University Halle-Wittenberg, Halle, Germany
Acta mathematica Universitatis Comenianae, Tome 90 (2021) no. 1, pp. 61-91
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Ján Filo; Volker Pluschke; Ján Filo; Volker Pluschke. An approximation of the nonlinear fluid--structure interaction problem for a rotationally symmetric flow. Acta mathematica Universitatis Comenianae, Tome 90 (2021) no. 1, pp. 61-91. http://geodesic.mathdoc.fr/item/AMUC_2021_90_1_a4/
@article{AMUC_2021_90_1_a4,
author = {J\'an Filo and Volker Pluschke and J\'an Filo and Volker Pluschke},
title = { An approximation of the nonlinear fluid--structure interaction problem for a rotationally symmetric flow},
journal = {Acta mathematica Universitatis Comenianae},
pages = {61--91},
year = {2021},
volume = {90},
number = {1},
url = {http://geodesic.mathdoc.fr/item/AMUC_2021_90_1_a4/}
}
TY - JOUR
AU - Ján Filo
AU - Volker Pluschke
AU - Ján Filo
AU - Volker Pluschke
TI - An approximation of the nonlinear fluid--structure interaction problem for a rotationally symmetric flow
JO - Acta mathematica Universitatis Comenianae
PY - 2021
SP - 61
EP - 91
VL - 90
IS - 1
UR - http://geodesic.mathdoc.fr/item/AMUC_2021_90_1_a4/
ID - AMUC_2021_90_1_a4
ER -
%0 Journal Article
%A Ján Filo
%A Volker Pluschke
%A Ján Filo
%A Volker Pluschke
%T An approximation of the nonlinear fluid--structure interaction problem for a rotationally symmetric flow
%J Acta mathematica Universitatis Comenianae
%D 2021
%P 61-91
%V 90
%N 1
%U http://geodesic.mathdoc.fr/item/AMUC_2021_90_1_a4/
%F AMUC_2021_90_1_a4
An approximation of the fluid-structure interaction problem in the cylindrical coordinate system is studied. First, we solve the free boundary problem by means of Schauder's fixed point theorem. After that, we regularize the linear viscoelastic cylindrical Koiter shell equation that was considered in [12], by adding higher order terms in order to get the strong convergence of the second derivatives of a sequence of radial displacements. We need the strong convergence of the second derivatives in order to guarantee the strong convergence of corresponding divergence free test functions due to [8].
