Determination of the 3D Navier-Stokes equations with nonlinear viscosity

Discrete and Continuous Dynamical Systems - S 2026 Open access

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Authors: Wenjia Zhao, Xin‐Guang Yang
DOI: 10.3934/dcdss.2026055
Cited by: 0
References: 15

Abstract

This paper investigates the long-time behavior of three-dimensional incompressible Navier-Stokes equations with nonlinear viscosity under periodic boundary conditions via determination. By employing energy estimates and Fourier-mode decomposition, we show that the system's asymptotic dynamics are fully determined by a finite set of low-frequency Fourier modes. We provide estimates for the number of modes in terms of the Grashof number for both autonomous and non-autonomous external forces.

Fields of Study & Subjects

Navier-Stokes equation solutions Stability and Controllability of Differential Equations Fluid Dynamics and Turbulent Flows

Publication details

Journal / source
Discrete and Continuous Dynamical Systems - S
Volume
30
Issue
0
Pages
295–315
Publication date
1 January 2026