Steady flows of Cosserat–Bingham fluids

Abstract

The equations describing the steady flow of Cosserat–Bingham fluids are considered, and existence of weak solution is proved for the three‐dimensional boundary‐value problem with the use of the Lipschitz truncation argument. In contrast to the classical Bingham fluid, the micropolar Bingham fluid supports local micro‐rotations and two types of plug zones. Our approach is based on an approximation of the constitutive relation by a generalized Newtonian constitutive relation and a subsequent limiting process. Copyright © 2016 John Wiley & Sons, Ltd.

Boundary control problems for nonlinear reaction-diffusion-convection model

“…Let us pass to the limit in (17) as m → ∞. From (15) it follows that all linear terms in (17) turn into corresponding ones in (16). Let us consider the nonlinear terms, starting with (k(φ m , •)φ m , h).…”

“…The current article contains the solvability of the boundary control problem, in which the role of control is played by the function ψ from the boundary condition (3). Also we should bear in mind that the papers [9,13,14] are generalizing the Boussinesq approximation for various models, while the papers [15][16][17] are dedicated to the study a number of complicated hydrodynamic models.…”

Theoretical Analysis of Boundary Value Problems for Generalized Boussinesq Model of Mass Transfer with Variable Coefficients

“…The global solvability of boundary value problem for the above mentioned mass transfer equations under non-homogeneous Dirichlet condition for the substance concentration was proved firstly in [24]. Let us note the papers [25][26][27][28][29][30], devoted to the study of non-stationary models, which generalize the Boussinesq approximation, as well as articles [31][32][33][34][35], in which a number of complicated hydrodynamic, including rheological, models was studied.…”