论文标题
具有随机谎言传输的3D Navier-Stokes方程的最大解决方案的存在和独特性
Existence and Uniqueness of Maximal Solutions to a 3D Navier-Stokes Equation with Stochastic Lie Transport
论文作者
论文摘要
我们在这里提出一个标准，可以得出结论，一个抽象的SPDE具有独特的最大强大解决方案，我们将其应用于三维随机Navier-Stokes方程。受[Kato and Lai，1984]在确定性环境中的工作的启发，我们在随机情况下提供了可比的结果，同时促进了多种噪声结构，例如添加剂，乘法和运输。尤其是我们的标准旨在拟合[Holm，2015]中介绍的Lie Transpest（SALT）的随机对流粘性流体动力学模型。我们对不可压缩的Navier-Stokes方程的应用与确定性理论的存在和独特性结果相匹配。这项简短的工作总结了结果，并宣布了两篇论文[Goodair等，2022]，这些论文为抽象良好的参数提供了全部细节，并将其应用于Navier-Stokes方程。
We present here a criterion to conclude that an abstract SPDE posseses a unique maximal strong solution, which we apply to a three dimensional Stochastic Navier-Stokes Equation. Inspired by the work of [Kato and Lai,1984] in the deterministic setting, we provide a comparable result here in the stochastic case whilst facilitating a variety of noise structures such as additive, multiplicative and transport. In particular our criterion is designed to fit viscous fluid dynamics models with Stochastic Advection by Lie Transport (SALT) as introduced in [Holm,2015]. Our application to the Incompressible Navier-Stokes equation matches the existence and uniqueness result of the deterministic theory. This short work summarises the results and announces two papers [Goodair et al, 2022] which give the full details for the abstract well-posedness arguments and application to the Navier-Stokes Equation.
