Author:
Goodair Daniel,Crisan Dan
Abstract
AbstractWe prove the existence and uniqueness of maximal solutions to the 3D SALT (Stochastic Advection by Lie Transport) Navier-Stokes Equation in velocity and vorticity form, on the torus and the bounded domain respectively. In particular we demonstrate the efficacy of Goodair et al. (Existence and Uniqueness of Maximal Solutions to SPDEs with Applications to Viscous Fluid Equations, 2023. Stochastics and Partial Differential Equations: Analysis and Computations, pp.1-64) in showing the well-posedness for both the velocity and vorticity form of the equation, as well as obtaining the first analytically strong existence result for a fluid equation perturbed by Lie transport noise on a bounded domain.
Publisher
Springer Nature Switzerland
Reference47 articles.
1. Agresti, A. and Veraar, M., 2021. Stochastic Navier-Stokes equations for turbulent flows in critical spaces. arXiv preprint arXiv:2107.03953.
2. Alonso-Orán, D. and Bethencourt de León, A., 2020. On the well-posedness of stochastic Boussinesq equations with transport noise. Journal of Nonlinear Science, 30(1), pp.175–224.
3. Attanasio, S. and Flandoli, F., 2011. Renormalized solutions for stochastic transport equations and the regularization by bilinear multiplicative noise. Communications in Partial Differential Equations, 36(8), pp.1455–1474.
4. Bensoussan, A. and Temam, R., 1973. Equations stochastiques du type Navier-Stokes. Journal of Functional Analysis, 13(2), pp.195–222.
5. Bethencourt-de-León, A. and Takao, S., 2022. Transport noise restores uniqueness and prevents blow-up in geometric transport equations. arXiv preprint arXiv:2211.14695.
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. Introduction;SpringerBriefs in Mathematics;2024
2. On the 3D Navier-Stokes Equations with Stochastic Lie Transport;Mathematics of Planet Earth;2023-08-04