Lange Theresa
Fakultät für Mathematik, Universität Bielefeld, 33501 Bielefeld, Germany.
J Dyn Differ Equ. 2024;36(4):3011-3036. doi: 10.1007/s10884-023-10255-5. Epub 2023 Mar 28.
In Tao 2016, the author constructs an averaged version of the deterministic three-dimensional Navier-Stokes equations (3D NSE) which experiences blow-up in finite time. In the last decades, various works have studied suitable perturbations of ill-behaved deterministic PDEs in order to prevent or delay such behavior. A promising example is given by a particular choice of stochastic transport noise closely studied in Flandoli et al. 2021. We analyze the model in Tao 2016 in view of these results and discuss the regularization skills of this noise in the context of the averaged 3D NSE.
在陶2016年的研究中，作者构建了确定性三维纳维-斯托克斯方程（3D NSE）的一个平均版本，该版本在有限时间内会出现爆破现象。在过去几十年里，各种研究致力于对表现不佳的确定性偏微分方程进行适当扰动，以防止或延迟这种行为。一个有前景的例子是由弗兰多利等人在2021年深入研究的一种特定随机输运噪声给出的。鉴于这些结果，我们分析了陶2016年的模型，并在平均3D NSE的背景下讨论了这种噪声的正则化技巧。
