论文标题
Riemann的非差异功能和二维曲率流动
Riemann's non-differentiable function and the binormal curvature flow
论文作者
论文摘要
我们在Riemann在1860年代引入的著名分析对象以及IT的某些变体之间建立了联系，而非线性几何PDE（二手曲率流量）。结果，该分析对象具有非明显的非线性几何解释。我们记得，二维流是涡旋丝演化的标准模型。我们证明了具有平滑轨迹的双向流动的溶液的存在，这些轨迹与需要的曲线一样近，具有多型曲线行为。最后，我们表明，这种行为属于弗里施和巴黎的多重形式，这些形式构想以控制湍流。
We make a connection between a famous analytical object introduced in the 1860s by Riemann, as well as some variants of it, and a nonlinear geometric PDE, the binormal curvature flow. As a consequence this analytical object has a non-obvious nonlinear geometric interpretation. We recall that the binormal flow is a standard model for the evolution of vortex filaments. We prove the existence of solutions of the binormal flow with smooth trajectories that are as close as desired to curves with a multifractal behavior. Finally, we show that this behavior falls within the multifractal formalism of Frisch and Parisi, which is conjectured to govern turbulent fluids.
