On the Lagrangian dynamics for the 3D incompressible Euler equations
type: Item
instance of: scholarly article
title: On the Lagrangian dynamics for the 3D incompressible Euler equations
zbMATH Open document ID: 1124.35062
published in: Communications in Mathematical Physics
publication date: 2007-05-31T00:00:00Z
review text: The dynamical behavior along the particle trajectories for some quantities of 3D inviscid incompressible fluids is studied. Evolution equations satisfied by scalar quantities composed of the spectrum of the deformation tensor, the Hessian of the pressure and the direction field of the vorticity are constructed. The dichotomy between the finite time singularity and the long time behavior of the various scalar quantities are studied.
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 76B03
Mathematics Subject Classification ID: 35Q05
zbMATH DE Number: 5159658
zbMATH Keywords: deformation tensor
zbMATH Keywords: pressure
zbMATH Keywords: vorticity
zbMATH Keywords: finite time singularity
zbMATH Keywords: long time behavior
author: Dongho Chae
MaRDI profile type: Publication
full work available at URL: s00220-006-0129-7
OpenAlex ID: W1975462157
cites work: Remarks on the breakdown of smooth solutions for the 3-D Euler equations
cites work: On the spectral dynamics of the deformation tensor and new a priori estimates for the 3D Euler equations
cites work: Remarks on the blow-up criterion of the three-dimensional Euler equations
cites work: Q4663544
cites work: On the well‐posedness of the Euler equations in the Triebel‐Lizorkin spaces
cites work: Geometric Statistics in Turbulence
cites work: Geometric constraints on potentially
cites work: On the collapse of tubes carried by 3D incompressible flows
cites work: Geometric Properties and Nonblowup of 3D Incompressible Euler Flow
cites work: Finite time singularities in ideal fluids with swirl
cites work: Nonstationary flows of viscous and ideal fluids in \(R^3\)
cites work: Evidence for a singularity of the three-dimensional, incompressible Euler equations
cites work: The critical Sobolev inequalities in Besov spaces and regularity criterion to some semi-linear evolution equations
cites work: Limiting case of the Sobolev inequality in BMO, with application to the Euler equations
cites work: Spectral dynamics of the velocity gradient field in restricted flows
cites work: Vorticity, Turbulence, and Acoustics in Fluid Flow
cites work: Vorticity and incompressible flow
cites work: On the Euler equations of incompressible perfect fluids
DOI: 10.1007/S00220-006-0129-7
description: scientific article; zbMATH DE number 5159658