论文标题
通过平均版本的Navier-Stokes方程的噪声正规化
Regularization by noise of an averaged version of the Navier-Stokes equations
论文作者
论文摘要
在Tao 2016中，作者构建了确定性三维Navier-Stokes方程（3D NSE）的平均版本，该方程式在有限的时间内经历了爆炸。在过去的几十年中，各种作品研究了不良行为的确定性PDE的适当扰动，以防止或延迟这种行为。在Flandoli等人中仔细研究的特定选择的随机运输噪声给出了一个有希望的例子。 2021年。鉴于这些结果，我们在TAO 2016中分析了该模型，并在平均3D NSE的背景下讨论了这种噪声的正则化技能。
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.
