On stationary thermo-rheological viscous flows

Abstract

We study the system of equations describing a stationary thermoconvective flow of a non-Newtonian fluid. We assume that the stress tensor S has the formwhere u is the vector velocity, P is the pressure, θ is the temperature and μ, p and τ are the given coefficients depending on the temperature. D and I are respectively the rate of strain tensor and the unit tensor. We prove the existence of a weak solution under general assumptions and the uniqueness under smallness conditions.

Existence and multiplicity results for elliptic problems with Nonlinear Boundary Conditions and variable exponents

“…This importance reflects directly into a various range of applications. There are applications concerning elastic materials [25], image restoration [7], thermorheological and electrorheological fluids [2,21] and mathematical biology [10].…”

Existence and multiplicity of $a$-harmonic solutions for a Steklov problem with variable exponents

“…This importance reflects directly into a various range of applications. There are applications concerning elastic materials [22], image restoration [11], thermorheological and electrorheological fluids [4,19] and mathematical biology [13].…”

Solutions of Nonlocal -Laplacian Equations

“…Problems with variable exponent growth conditions also appear in the modelling of stationary thermorheological viscous flows of non-Newtonian fluids and in the mathematical description of the processes of filtration of an ideal barotropic gas through a porous medium. The detailed application backgrounds of the ( )-Laplacian can be found in [10][11][12][13][14] and the references therein.…”