The existence of a weak solution for a compressible multicomponent fluid structure interaction problem

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00584372" target="_blank" >RIV/67985840:_____/24:00584372 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.matpur.2024.02.007" target="_blank" >https://doi.org/10.1016/j.matpur.2024.02.007</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.matpur.2024.02.007" target="_blank" >10.1016/j.matpur.2024.02.007</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The existence of a weak solution for a compressible multicomponent fluid structure interaction problem

Popis výsledku v původním jazyce

We analyze a system of PDEs governing the interaction between two compressible mutually noninteracting fluids and a shell of Koiter type encompassing a time dependent 3D domain filled by the fluids. The dynamics of the fluids is modeled by a system resembling compressible Navier-Stokes equations with a physically realistic pressure depending on densities of both the fluids. The shell possesses a non-linear, non-convex Koiter energy. Considering that the densities are comparable initially we prove the existence of a weak solution until the degeneracy of the energy or the self-intersection of the structure occurs for two cases. In the first case the adiabatic exponents are assumed to satisfy max⁡{γ,β}>2, min⁡{γ,β}>0, and the structure involved is assumed to be non-dissipative. For the second case we assume the critical case max⁡{γ,β}≥2 and min⁡{γ,β}>0 and the dissipativity of the structure. The result is achieved in several steps involving, extension of the physical domain, penalization of the interface condition, artificial regularization of the shell energy and the pressure, the almost compactness argument, added structural dissipation and suitable limit passages depending on uniform estimates.

Název v anglickém jazyce

The existence of a weak solution for a compressible multicomponent fluid structure interaction problem

Popis výsledku anglicky

We analyze a system of PDEs governing the interaction between two compressible mutually noninteracting fluids and a shell of Koiter type encompassing a time dependent 3D domain filled by the fluids. The dynamics of the fluids is modeled by a system resembling compressible Navier-Stokes equations with a physically realistic pressure depending on densities of both the fluids. The shell possesses a non-linear, non-convex Koiter energy. Considering that the densities are comparable initially we prove the existence of a weak solution until the degeneracy of the energy or the self-intersection of the structure occurs for two cases. In the first case the adiabatic exponents are assumed to satisfy max⁡{γ,β}>2, min⁡{γ,β}>0, and the structure involved is assumed to be non-dissipative. For the second case we assume the critical case max⁡{γ,β}≥2 and min⁡{γ,β}>0 and the dissipativity of the structure. The result is achieved in several steps involving, extension of the physical domain, penalization of the interface condition, artificial regularization of the shell energy and the pressure, the almost compactness argument, added structural dissipation and suitable limit passages depending on uniform estimates.

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

2024

Kód důvěrnosti údajů

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

Název periodika

Journal de Mathematiques Pures et Appliquees

ISSN

0021-7824

e-ISSN

1776-3371

Svazek periodika

184

Číslo periodika v rámci svazku

April

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

72

Strana od-do

118-189

Kód UT WoS článku

001206877700001

EID výsledku v databázi Scopus

2-s2.0-85187641241