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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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).

Název v anglickém jazyce

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

Popis výsledku anglicky

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).

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/LL1202" target="_blank" >LL1202: Materiály s implicitními konstitutivními vztahy: Od teorie přes redukci modelů k efektivním numerickým metodám</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

Vietnam Journal of Mathematics

ISSN

2305-221X

e-ISSN

—

Svazek periodika

45

Číslo periodika v rámci svazku

1-2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

14

Strana od-do

207-220

Kód UT WoS článku

000393860800010

EID výsledku v databázi Scopus

2-s2.0-85010840283