On steady third grade fluids equations

Abstract

Abstract. Let Ω be a simply connected, bounded, smooth domain of R 2 or R 3 . We consider the equation of steady motion of a third grade fluid in Ω with homogeneous Dirichlet boundary conditions. We prove that the monotonicity technique used by Paicu [17] in the full space for unsteady motion allows to obtain the existence of a W 1,4 0 solution provided that the forcing belongs to W −1, 4 3 . The size of the forcing is arbitrary.

Existence of weak solutions for steady viscous fluids with general slip boundary conditions

“…Besides, there are some works done on more general hypotheses on the stress tensor T , on bipolar viscous fluids or on second or even third grade flows, see [18,19,5,[20][21][22].…”

The Unique Existence of Weak Solution and the Optimal Control for Time‐Fractional Third Grade Fluid System

“…This can be achieved by the monotony method as in [8,34]; see also [35,36]. Indeed, since T 1 ( ) is uniformly (in ) bounded in 4/3 (0, ; W * ), we may assume that…”

Effects of Slip Condition, Variable Viscosity and Inclined Magnetic Field on the Peristaltic Motion of a Non-Newtonian Fluid in an Inclined Asymmetric Channel

“…(Busuioc et al ) proved a mathematical theory of existence and uniqueness of solutions for the constitutive law 5 with some restrictions on the material coefficients. In this discussion, we have considered some limitations on these coefficients, in a manner similar to (Busuioc et al ;Ali et al 2009). The first three Rivlin Ericksen tensors can be written as…”