We show that the spatial Lq-norm (q > 5/3) of the vorticity of an incompressible viscous fluid in ℝ3 remains bounded uniformly in time, provided that the direction of vorticity is Holder continuous in space, and that the space-time Lq-norm of vorticity is finite. The Holder 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 Grujic-Ruzmaikina (Interpolation between algebraic and geometric conditions for smoothness of the vorticity in the 3D NSE, Indiana Univ. J. Math. 53 (2004), 1073–1080).

中文翻译：

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关于不可压缩粘性流体中的涡流排列和涡量 Lq 范数的有界性

我们表明，ℝ3 中不可压缩粘性流体的涡量的空间 Lq 范数 (q > 5/3) 在时间上保持均匀有界，前提是涡量的方向在空间中是 Holder 连续的，并且时空 Lq -涡量范数是有限的。持有人指数仅取决于 q。这是 Constantin-Fefferman 经典结果的变体（Navier-Stokes 方程的涡度方向和全局规律性问题，Indiana Univ. J. Math. 42 (1993), 775–789），以及相关的Grujic-Ruzmaikina 的工作（代数和几何条件之间的插值，用于 3D NSE 中涡度的平滑度，印第安纳大学 J. 数学 53（2004），1073-1080）。