On Existence analysis of steady flows of generalized Newtonian fluids with concentration dependent power-law index

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F13%3A10139892" target="_blank" >RIV/00216208:11320/13:10139892 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jmaa.2012.12.066" target="_blank" >http://dx.doi.org/10.1016/j.jmaa.2012.12.066</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmaa.2012.12.066" target="_blank" >10.1016/j.jmaa.2012.12.066</a>

Result language
angličtina
Original language name
On Existence analysis of steady flows of generalized Newtonian fluids with concentration dependent power-law index
Original language description
We study a system of partial differential equations describing a steady flow of an incompressible generalized Newtonian fluid, wherein the Cauchy stress is concentration dependent. Namely, we consider a coupled system of the generalized Navier-Stokes equations and convection-diffusion equation with non-linear diffusivity. We prove the existence of a weak solution for certain class of models by using a generalization of the monotone operator theory which fits into the framework of generalized Sobolev spaces with variable exponent. Such a framework is involved since the function spaces, where we look for the weak solution, are "dependent" of the solution itself, and thus, we a priori do not know them. This leads us to the principal a priori assumptions on the model parameters that ensure the Wilder continuity of the variable exponent. We present here a constructive proof based on the Galerkin method that allows us to obtain the result for very general class of models.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GA201%2F09%2F0917" target="_blank" >GA201/09/0917: Mathematical and computer analysis of the evolution processes in nonlinear viscoelastic fluid-like materials</a><br>
Continuities
S - Specificky vyzkum na vysokych skolach

Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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