Coupling the Navier-Stokes-Fourier equations with the Johnson-Segalman stress-diffusive viscoelastic model: Global-in-time and large-data analysis

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10490284" target="_blank" >RIV/00216208:11320/24:10490284 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Zjc9bdFrqj" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Zjc9bdFrqj</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1142/S0218202524500064" target="_blank" >10.1142/S0218202524500064</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Coupling the Navier-Stokes-Fourier equations with the Johnson-Segalman stress-diffusive viscoelastic model: Global-in-time and large-data analysis

Popis výsledku v původním jazyce

We prove that there exists a large-data and global-in-time weak solution to a system of partial differential equations describing the unsteady flow of an incompressible heat-conducting rate-type viscoelastic stress-diffusive fluid filling up a mechanically and thermally isolated container of any dimension. To overcome the principal difficulties connected with ill-posedness of the diffusive Oldroyd-B model in three dimensions, we assume that the fluid admits a strengthened dissipation mechanism, at least for excessive elastic deformations. All the relevant material coefficients are allowed to depend continuously on the temperature, whose evolution is captured by a thermodynamically consistent equation. In fact, the studied model is derived from scratch using only the balance equations for linear momentum and energy, the formulation of the second law of thermodynamics and the constitutive equation for the internal energy. The latter is assumed to be a linear function of temperature, which simplifies the model. The concept of our weak solution incorporates both the temperature and entropy inequalities, and also the local balance of total energy provided that the pressure function exists.

Název v anglickém jazyce

Coupling the Navier-Stokes-Fourier equations with the Johnson-Segalman stress-diffusive viscoelastic model: Global-in-time and large-data analysis

Popis výsledku anglicky

We prove that there exists a large-data and global-in-time weak solution to a system of partial differential equations describing the unsteady flow of an incompressible heat-conducting rate-type viscoelastic stress-diffusive fluid filling up a mechanically and thermally isolated container of any dimension. To overcome the principal difficulties connected with ill-posedness of the diffusive Oldroyd-B model in three dimensions, we assume that the fluid admits a strengthened dissipation mechanism, at least for excessive elastic deformations. All the relevant material coefficients are allowed to depend continuously on the temperature, whose evolution is captured by a thermodynamically consistent equation. In fact, the studied model is derived from scratch using only the balance equations for linear momentum and energy, the formulation of the second law of thermodynamics and the constitutive equation for the internal energy. The latter is assumed to be a linear function of temperature, which simplifies the model. The concept of our weak solution incorporates both the temperature and entropy inequalities, and also the local balance of total energy provided that the pressure function exists.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GX20-11027X" target="_blank" >GX20-11027X: Matematická analýza parciálních diferenciálních rovnic popisujících silně nerovnovážné stavy v otevřených systémech termodynamiky kontinua</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

Mathematical Models and Methods in Applied Sciences

ISSN

0218-2025

e-ISSN

1793-6314

Svazek periodika

34

Číslo periodika v rámci svazku

03

Stát vydavatele periodika

SG - Singapurská republika

Počet stran výsledku

60

Strana od-do

417-476

Kód UT WoS článku

001146302500001

EID výsledku v databázi Scopus

2-s2.0-85183532393