Determining modes for the 3D Navier-Stokes equations

PHYSICA D-NONLINEAR PHENOMENA

卷:374

Article

Cheskidov, Alexey¹  Dai, Mimi²  Kavlie, Landon¹ 

[1] Univ Illinois, Dept Math Stat & Comp Sci, Chicago, IL 60607 USA

[2] Univ Illinois, Dept Appl Math Stat & Comp Sci, Chicago, IL 60607 USA

关键词: Navier-Stokes equations;    Determining modes;    Global attractor;   

DOI  :  10.1016/j.physd.2017.11.014

来源: Elsevier

【 摘 要 】

We introduce a determining wavenumber for the forced 3D Navier-Stokes equations (NSE) defined for each individual solution. Even though this wavenumber blows up if the solution blows up, its time average is uniformly bounded for all solutions on the weak global attractor. The bound is compared to Kolmogorov's dissipation wavenumber and the Grashof constant. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free