Global Well-Posedness for Two-Dimensional Flows of Viscoelastic Rate-Type Fluids with Stress Diffusion

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10452919" target="_blank" >RIV/00216208:11320/22:10452919 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=jC60qpSH_p" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=jC60qpSH_p</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00021-022-00696-1" target="_blank" >10.1007/s00021-022-00696-1</a>

Result language
angličtina
Original language name
Global Well-Posedness for Two-Dimensional Flows of Viscoelastic Rate-Type Fluids with Stress Diffusion
Original language description
We consider the system of partial differential equations governing two-dimensional flows of a robust class of viscoelastic rate-type fluids with stress diffusion, involving a general objective derivative. The studied system generalizes the incompressible Navier-Stokes equations for the fluid velocity v and pressure p by the presence of an additional term in the constitutive equation for the Cauchy stress expressed in terms of a positive definite tensor B. The tensor B evolves according to a diffusive variant of an equation that can be viewed as a combination of corresponding counterparts of Oldroyd-B and Giesekus models. Considering spatially periodic problem, we prove that for arbitrary initial data and forcing in appropriate L-2 spaces, there exists a unique globally defined weak solution to the equations of motion, and more regular initial data and forcing launch a more regular solution with B positive definite everywhere.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GX20-11027X" target="_blank" >GX20-11027X: Mathematical analysis of partial differential equations describing far-from-equilibrium open systems in continuum thermodynamics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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