Internal Flows of Incompressible Fluids Subject to Stick-Slip Boundary Conditions

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10367390" target="_blank" >RIV/00216208:11320/17:10367390 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s10013-016-0221-z" target="_blank" >http://dx.doi.org/10.1007/s10013-016-0221-z</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10013-016-0221-z" target="_blank" >10.1007/s10013-016-0221-z</a>

Result language
angličtina
Original language name
Internal Flows of Incompressible Fluids Subject to Stick-Slip Boundary Conditions
Original language description
We study mathematical properties of internal three-dimensional flows of incompressible heat-conducting fluids with stick-slip boundary conditions, which state that the fluid adheres to the boundary until a certain criterion activates the slipping regime on the boundary. We look at this type of activated boundary condition as at an implicit constitutive equation on the boundary and establish the long-time and large-data existence of weak solutions for the incompressible three-dimensional Navier-Stokes-Fourier system with the viscosity and the heat conductivity depending on the temperature (internal energy). It is essential for our approach to know that the pressure, i.e., the quantity that is a consequence of the fact that the material is incompressible, is globally integrable. While this requirement is in the case of unsteady flows subject to a no-slip boundary condition open for most incompressible fluids, we show that this difficulty can be successfully overcome if one replaces the no-slip boundary condition by a stick-slip boundary condition. The result relies also on the approach developed in Buliek et al. (Nonlinear Anal. Real World Appl. 10, 992-1015, 2009).
Czech name
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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
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/LL1202" target="_blank" >LL1202: Implicitly constituted material models: from theory through model reduction to efficient numerical methods</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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