ON INCOMPRESSIBLE HEAT-CONDUCTING VISCOELASTIC RATE-TYPE FLUIDS WITH STRESS-DIFFUSION AND PURELY SPHERICAL ELASTIC RESPONSE
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
ON INCOMPRESSIBLE HEAT-CONDUCTING VISCOELASTIC RATE-TYPE FLUIDS WITH STRESS-DIFFUSION AND PURELY SPHERICAL ELASTIC RESPONSE
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA18-12719S" target="_blank" >GA18-12719S: Thermodynamical and mathematical analysis of flows of complex fluids</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
SIAM Journal on Mathematical Analysis
ISSN
0036-1410
e-ISSN
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Volume of the periodical
53
Issue of the periodical within the volume
4
Country of publishing house
US - UNITED STATES
Number of pages
46
Pages from-to
3985-4030
UT code for WoS article
000692288300010
EID of the result in the Scopus database
2-s2.0-85112670847