论文标题
在涡流纸上集中精力
On concentration in vortex sheets
论文作者
论文摘要
回顾了带有涡旋形式初始数据的二维不可压欧方程的近似解决方案序列中的能量浓度问题。涡度最大功能是基于结构函数的新身份，提出是一种定量工具，以检测近似溶液序列中的浓度效应。如\ emph {[R.〜Krasny，J。Fluid Mech中引入的那样，该工具都应用于基于Vortex-Blob方法的数值实验，其中考虑了无划分符号的初始数据。 \ textbf {167}：65-93（1986）]}。数值证据表明，对于被考虑的初始数据，没有能量浓度出现在零斑点验证$ε\至0 $的极限中。
The question of energy concentration in approximate solution sequences $u^ε$, as $ε\to 0$, of the two-dimensional incompressible Euler equations with vortex-sheet initial data is revisited. Building on a novel identity for the structure function in terms of vorticity, the vorticity maximal function is proposed as a quantitative tool to detect concentration effects in approximate solution sequences. This tool is applied to numerical experiments based on the vortex-blob method, where vortex sheet initial data without distinguished sign are considered, as introduced in \emph{[R.~Krasny, J. Fluid Mech. \textbf{167}:65-93 (1986)]}. Numerical evidence suggests that no energy concentration appears in the limit of zero blob-regularization $ε\to 0$, for the considered initial data.
