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

2023/01/19 by Dalibor Pražák, Prazak, Dalibor, Buddhika Priyasad +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2301.08112

openalex publication_date 2023/01/19 · openalex created_date 2023/01/21 · openalex updated_date 2026/07/28

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.

Related

• On the attractor for 2D Navier-Stokes-like system with the dynamic slip boundary condition in a channel
• Strong solutions and attractor dimension for 2D NSE with dynamic boundary conditions
• On an attractor for strong solutions to interactive fluid-plate system without rotational inertia
• Finite dimensionality of global attractor for the solutions to 3D viscous primitive equations of large-scale moist atmosphere
• Upper bounds on the dimension of the global attractor of the 2D Navier-Stokes equations on the β-plane