On depletion of the vortex-stretching term in the 3D Navier-Stokes equations
type: Item
instance of: scholarly article
title: On depletion of the vortex-stretching term in the 3D Navier-Stokes equations
zbMATH Open document ID: 1091.35061
author: Zoran Grujić
author: Anastasia A. Ruzmaikina
published in: Communications in Mathematical Physics
publication date: 2004-11-11T00:00:00Z
review text: This is a very interesting paper concerning the regularity of 3D Navier-Stokes solutions. It is based on an integral representation of the stretching factor of the vorticity evolution, given by \textit{P. Constantin} [SIAM Rev. 36, No. 1, 73--98 (1994; Zbl 0803.35106)]. This result and some new cancellation properties are used for obtaining new properties in the vortex-stretching. A new geometric criteria for preventing finite-time blow-up of N-S solutions is given. An isotropy condition is detected, which can control the evolution of enstrophy. In section 3, a rigorous analysis of enstrophy is given, specifying the control on small and large scales, related with Kolmogorov's theory. Some useful estimates are given in section 4. The main theorem, giving a condition for non-blow-up of vorticity, is proved in the last section.
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 76D03
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 76F60
zbMATH DE Number: 2114616
zbMATH Keywords: blow-up time
zbMATH Keywords: regularity
zbMATH Keywords: enstrophy
zbMATH Keywords: scales
zbMATH Keywords: vorticity
reviewed by: Gelu Paşa
MaRDI profile type: Publication
full work available at URL: s00220-004-1072-0
OpenAlex ID: W1972880234
DOI: 10.1007/S00220-004-1072-0
Recommended article: Vortex stretching and enhanced dissipation for the incompressible 3D Navier-Stokes equations
Recommended article: Vortex stretching and criticality for the three-dimensional Navier-Stokes equations
Recommended article: Dynamic depletion of vortex stretching and non-blowup of the 3-D incompressible Euler equations
Recommended article: Geometric depletion of vortex stretch in 3d viscous incompressible flow
Recommended article: Vortex stretching and anisotropic diffusion in the 3D Navier-Stokes equations
Recommended article: Stretching and compression of vorticity in the 3D Euler equations
Recommended article: Dynamically stretched vortices as solutions of the 3D Navier-Stokes equations
Recommended article: Asymptotic solutions of the Navier-Stokes equations and systems of stretched vortices filling a three-dimensional volume
Recommended article: Quasi-streamwise vortices and enhanced dissipation for incompressible 3D Navier–Stokes equations
Recommended article: Q3986723
description: scientific article; zbMATH DE number 2114616