Existence and regularity of weak solutions for a fluid interacting with a non-linear shell in three dimensions

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10475836" target="_blank" >RIV/00216208:11320/22:10475836 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=k.9E6Srl8x" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=k.9E6Srl8x</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4171/AIHPC/33" target="_blank" >10.4171/AIHPC/33</a>

Result language
angličtina
Original language name
Existence and regularity of weak solutions for a fluid interacting with a non-linear shell in three dimensions
Original language description
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 (with respect to terms of highest order). The estimates are obtained by introducing new analytical tools that allow dissipative effects of the fluid to be exploited for the (non-dissipative) solid. The regularity result depends on the geometric constitution alone and is independent of the approximation proce-dure; 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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical
Annales de l'Institut Henri Poincaré C, Analyse Non Linéaire
ISSN
0294-1449
e-ISSN
1873-1430
Volume of the periodical
39
Issue of the periodical within the volume
6
Country of publishing house
FR - FRANCE
Number of pages
44
Pages from-to
1369-1412
UT code for WoS article
000927008900003
EID of the result in the Scopus database
2-s2.0-85147381275

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