典型文献
On Some Properties of the Curl Operator and Their Consequences for the Navier-Stokes System
文献摘要：
We investigate some geometric properties of the curl operator,based on its diagonalization and its expression as a non-local symmetry of the pseudo-derivative(-Δ)1/2 among divergence-free vector fields with finite energy.In this context,we introduce the notion of spin-definite fields,i.e.eigenvectors of(-Δ)-1/2curl.The two spin-definite components of a general 3D incompress-ible flow untangle the right-handed motion from the left-handed one.Having observed that the non-linearity of Navier-Stokes has the structure of a cross-product and its weak(distributional)form is a determinant that involves the vorticity,the velocity and a test function,we revisit the conservation of energy and the balance of helicity in a geometrical fashion.We show that in the case of a finite-time blow-up,both spin-definite components of the flow will explode simultaneously and with equal rates,i.e.singularities in 3D are the result of a conflict of spin,which is impossible in the poorer geometry of 2D flows.We investigate the role of the local and non-local determinants∫T0∫R3det(curlu,u,(-Δ)θu)and their spin-definite counterparts,which drive the enstrophy and,more gen-erally,are responsible for the regularity of the flow and the emergence of sin-gularities or quasi-singularities.As such,they are at the core of turbulence phenomena.
文献关键词：
中图分类号：
作者姓名：
Nicolas Lerner;Fran?ois Vigneron
作者机构：
Sorbonne Université,Institut de Mathématiques de Jussieu,UMR 7586,Campus Pierre et Marie Curie,4 Place Jussieu,75252 Paris cedex 05,France;Université de Reims Champagne-Ardenne,Laboratoire de Mathématiques de Reims,UMR 9008,Moulin de la Housse,BP 1039,51687 Reims cedex 2,France
文献出处：
引用格式：
[1]Nicolas Lerner;Fran?ois Vigneron-.On Some Properties of the Curl Operator and Their Consequences for the Navier-Stokes System)[J].数学研究通讯,2022(04):449-497
A类：
2curl,incompress,untangle,R3det,curlu,enstrophy,gularities
B类：
On,Some,Properties,Curl,Operator,Their,Consequences,Navier,Stokes,System,We,investigate,some,properties,operator,its,diagonalization,expression,local,symmetry,pseudo,derivative,among,divergence,free,fields,energy,In,this,context,introduce,notion,spin,definite,eigenvectors,two,components,general,right,handed,motion,from,left,Having,observed,that,linearity,has,structure,cross,product,weak,distributional,form,involves,vorticity,velocity,test,function,revisit,conservation,balance,helicity,geometrical,fashion,show,case,blow,up,both,will,explode,simultaneously,equal,rates,singularities,are,result,conflict,which,impossible,poorer,geometry,2D,flows,role,determinants,T0,their,counterparts,drive,more,erally,responsible,regularity,emergence,quasi,such,they,core,turbulence,phenomena
AB值：
0.547769
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