ON INCOMPRESSIBLE HEAT-CONDUCTING VISCOELASTIC RATE-TYPE FLUIDS WITH STRESS-DIFFUSION AND PURELY SPHERICAL ELASTIC RESPONSE

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10435824" target="_blank" >RIV/00216208:11320/21:10435824 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=jVUIRN1fz4" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=jVUIRN1fz4</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/20M1384452" target="_blank" >10.1137/20M1384452</a>

Jazyk výsledku

angličtina

Název v původním jazyce

ON INCOMPRESSIBLE HEAT-CONDUCTING VISCOELASTIC RATE-TYPE FLUIDS WITH STRESS-DIFFUSION AND PURELY SPHERICAL ELASTIC RESPONSE

Popis výsledku v původním jazyce

We prove the existence of large-data global-in-time weak solutions to an evolutionary PDE system describing flows of incompressible heat-conducting viscoelastic rate-type fluids with stress-diffusion, subject to a stick-slip boundary condition for the velocity and a homogeneous Neumann boundary condition for the extra stress tensor. In the introductory section we develop the thermodynamic foundations of the proposed model, and we document the role of thermodynamics in obtaining critical structural relations between the quantities of interest. These structural relations are then exploited in the mathematical analysis of the governing equations. In particular, the definition of weak solution is motivated by the thermodynamic basis of the model. The extra stress tensor describing the elastic response of the fluid is in our case purely spherical, which is a simplification from the physical point of view. The model nevertheless exhibits features that require novel mathematical ideas in order to deal with the technically complex structure of the associated internal energy and the more complicated forms of the corresponding entropy and energy fluxes. The paper provides the first rigorous proof of the existence of large-data global-in-time weak solutions to the governing equations for coupled thermo-mechanical processes in viscoelastic rate-type fluids.

Název v anglickém jazyce

ON INCOMPRESSIBLE HEAT-CONDUCTING VISCOELASTIC RATE-TYPE FLUIDS WITH STRESS-DIFFUSION AND PURELY SPHERICAL ELASTIC RESPONSE

Popis výsledku anglicky

We prove the existence of large-data global-in-time weak solutions to an evolutionary PDE system describing flows of incompressible heat-conducting viscoelastic rate-type fluids with stress-diffusion, subject to a stick-slip boundary condition for the velocity and a homogeneous Neumann boundary condition for the extra stress tensor. In the introductory section we develop the thermodynamic foundations of the proposed model, and we document the role of thermodynamics in obtaining critical structural relations between the quantities of interest. These structural relations are then exploited in the mathematical analysis of the governing equations. In particular, the definition of weak solution is motivated by the thermodynamic basis of the model. The extra stress tensor describing the elastic response of the fluid is in our case purely spherical, which is a simplification from the physical point of view. The model nevertheless exhibits features that require novel mathematical ideas in order to deal with the technically complex structure of the associated internal energy and the more complicated forms of the corresponding entropy and energy fluxes. The paper provides the first rigorous proof of the existence of large-data global-in-time weak solutions to the governing equations for coupled thermo-mechanical processes in viscoelastic rate-type fluids.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA18-12719S" target="_blank" >GA18-12719S: Thermodynamická a matematická analýza proudění strukturovaných tekutin</a><br>

Návaznosti

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

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název periodika

SIAM Journal on Mathematical Analysis

ISSN

0036-1410

e-ISSN

—

Svazek periodika

53

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

46

Strana od-do

3985-4030

Kód UT WoS článku

000692288300010

EID výsledku v databázi Scopus

2-s2.0-85112670847