ON VORTEX ALIGNMENT AND THE BOUNDEDNESS OF THE Lq-NORM OF VORTICITY IN INCOMPRESSIBLE VISCOUS FLUIDS  

作　　者：Siran LI 李思然(Department of Mathematics,Rice University,MS 136 P.O.Box 1892,Houston,Texas,77251,USA;Current Address:Department of Mathematics,New York University-Shanghai,office 1146,1555 Century Avenue,Pudong,Shanghai 200122,China)

机构地区：[1]Department of Mathematics,Rice University,MS 136 P.O.Box 1892,Houston,Texas,77251,USA [2]Current Address:Department of Mathematics,New York University-Shanghai,office 1146,1555 Century Avenue,Pudong,Shanghai 200122,China

出　　处：《Acta Mathematica Scientia》2020年第6期1700-1708,共9页数学物理学报（B辑英文版）

摘　　要：We show that the spatial L q-norm(q>5/3)of the vorticity of an incompressible viscous fluid in R^3 remains bounded uniformly in time,provided that the direction of vorticity is Hölder continuous in space,and that the space-time L q-norm of vorticity is finite.The Hölder index depends only on q.This serves as a variant of the classical result by Constantin-Fefferman(Direction of vorticity and the problem of global regularity for the Navier-Stokes equations,Indiana Univ.J.Math.42(1993),775-789),and the related work by Grujić-Ruzmaikina(Interpolation between algebraic and geometric conditions for smoothness of the vorticity in the 3D NSE,Indiana Univ.J.Math.53(2004),1073-1080).

关 键 词：Navier-Stokes equations VORTICITY regularity vortex alignment weak solution strong solution incompressible fluid 

分 类 号：O357.1[理学—流体力学] O175[理学—力学]