On time-periodic solutions to an interaction problem between compressible viscous fluids and viscoelastic beams

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F25%3A00602401" target="_blank" >RIV/67985840:_____/25:00602401 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1088/1361-6544/ad92f0" target="_blank" >https://doi.org/10.1088/1361-6544/ad92f0</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1088/1361-6544/ad92f0" target="_blank" >10.1088/1361-6544/ad92f0</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On time-periodic solutions to an interaction problem between compressible viscous fluids and viscoelastic beams

Popis výsledku v původním jazyce

In this paper, we study a nonlinear fluid-structure interaction problem between a 'square-root' viscoelastic beam and a compressible viscous fluid. The beam is immersed in the fluid which fills a two-dimensional rectangular domain with periodic boundary conditions in both directions, while both the beam and the fluid are under the effect of time-periodic forces. By using a decoupling approach, at least one time-periodic weak solution to this problem is constructed which has a bounded energy and a fixed prescribed mass. The lack of a priori energy bounds is overcome by a series of estimates based on a careful choice of parameters. The most challenging one is the pressure estimate, which is obtained by utilizing the specific periodic geometry and the Bogovski operator on a fixed domain that has a uniform constant. With uniform estimates and improved regularity of the beam as in (Muha and Schwarzacher 2023Ann. Inst. Henri Poin. Anal. Non Lineaire 39 1369-412), the time-periodic solutionis constructed by a series of limit procedures, following the finite-dimensional time-space construction from (Feireislet al 2012 Arch. Rational Mech. Anal. 204 74586).

Název v anglickém jazyce

On time-periodic solutions to an interaction problem between compressible viscous fluids and viscoelastic beams

Popis výsledku anglicky

In this paper, we study a nonlinear fluid-structure interaction problem between a 'square-root' viscoelastic beam and a compressible viscous fluid. The beam is immersed in the fluid which fills a two-dimensional rectangular domain with periodic boundary conditions in both directions, while both the beam and the fluid are under the effect of time-periodic forces. By using a decoupling approach, at least one time-periodic weak solution to this problem is constructed which has a bounded energy and a fixed prescribed mass. The lack of a priori energy bounds is overcome by a series of estimates based on a careful choice of parameters. The most challenging one is the pressure estimate, which is obtained by utilizing the specific periodic geometry and the Bogovski operator on a fixed domain that has a uniform constant. With uniform estimates and improved regularity of the beam as in (Muha and Schwarzacher 2023Ann. Inst. Henri Poin. Anal. Non Lineaire 39 1369-412), the time-periodic solutionis constructed by a series of limit procedures, following the finite-dimensional time-space construction from (Feireislet al 2012 Arch. Rational Mech. Anal. 204 74586).

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA22-01591S" target="_blank" >GA22-01591S: Matematická teorie a numerická analýza rovnic vazkých newtonovských stlačitelných tekutin</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

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

Název periodika

Nonlinearity

ISSN

0951-7715

e-ISSN

1361-6544

Svazek periodika

38

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

48

Strana od-do

015005

Kód UT WoS článku

001364644100001

EID výsledku v databázi Scopus

2-s2.0-85216284765