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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Annales de l&apos;Institut Henri Poincaré C, Analyse Non Linéaire

ISSN

0294-1449

e-ISSN

1873-1430

Svazek periodika

39

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

FR - Francouzská republika

Počet stran výsledku

44

Strana od-do

1369-1412

Kód UT WoS článku

000927008900003

EID výsledku v databázi Scopus

2-s2.0-85147381275