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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:402

Article

Bulicek, Miroslav¹  Pustejovska, Petra^1,2 

[1] Charles Univ Prague, Fac Math & Phys, Math Inst, Prague 18675 8, Czech Republic

[2] Graz Univ Technol, Inst Computat Math, Steyrergasse 30-3, A-8010 Graz, Austria

关键词: Generalized Navier-Stokes system;    Incompressible fluid;    Concentration dependent viscosity;    Shear-rate dependent viscosity;    Sobolev spaces with variable exponent;   

DOI  :  10.1016/j.jmaa.2012.12.066

来源: Elsevier

【 摘 要 】

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. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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