The Existence and Dimension of the Attractor for a 3D Flow of a Non-Newtonian Fluid subject to Dynamic Boundary Conditions

TL;DR

This paper proves the existence and estimates the dimension of the global attractor for a 3D non-Newtonian fluid flow with dynamic boundary conditions, linking mathematical properties to physical parameters.

Contribution

It provides explicit dimension estimates of the global attractor for Ladyzhenskaya type fluids under dynamic boundary conditions, advancing understanding of long-term behavior.

Findings

Explicit dimension bounds of the global attractor derived

Conditions on stress tensor growth rate established

Mathematical results connect physical parameters to attractor complexity

Abstract

We consider non-Newtonian incompressible 3D fluid of Ladyzhenskaya type, in the setting of the dynamic boundary condition. Assuming sufficient growth rate of the stress tensor with respect to the velocity gradient, we establish explicit dimension estimate of the global attractor in terms of the physical parameters of the problem.