Kolmogorov's dissipation number and the number of degrees of freedom for the 3D Navier–Stokes equations
| Autor: | Mimi Dai, Alexey Cheskidov |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
General Mathematics
Mathematics::Analysis of PDEs FOS: Physical sciences 35Q35 37L30 01 natural sciences law.invention Physics::Fluid Dynamics Mathematics - Analysis of PDEs law Intermittency Attractor FOS: Mathematics Fluid dynamics Wavenumber 0101 mathematics Navier–Stokes equations Physics Turbulence 010102 general mathematics Mathematical analysis Degrees of freedom Fluid Dynamics (physics.flu-dyn) Physics - Fluid Dynamics Nonlinear Sciences::Chaotic Dynamics 010101 applied mathematics Bounded function Analysis of PDEs (math.AP) |
| Zdroj: | Proceedings of the Royal Society of Edinburgh: Section A Mathematics. 149:429-446 |
| ISSN: | 1473-7124 0308-2105 |
| DOI: | 10.1017/prm.2018.33 |
| Popis: | Kolmogorov's theory of turbulence predicts that only wavenumbers below some critical value, called Kolmogorov's dissipation number, are essential to describe the evolution of a three-dimensional fluid flow. A determining wavenumber, first introduced by Foias and Prodi for the 2D Navier-Stokes equations, is a mathematical analog of Kolmogorov's number. The purpose of this paper is to prove the existence of a time-dependent determining wavenumber for the 3D Navier-Stokes equations whose time average is bounded by Kolmogorov's dissipation wavenumber for all solutions on the global attractor whose intermittency is not extreme. Revised version |
| Databáze: | OpenAIRE |
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