Mean-square approximation of Navier-Stokes equations with additive noise in vorticity-velocity formulation

Milstein, G N; Tretyakov, M V

Abstract

We consider a time discretization of incompressible Navier-Stokes equations with spatial periodic boundary conditions and additive noise in the vorticity-velocity formulation. The approximation is based on freezing the velocity on time subintervals resulting in a linear stochastic parabolic equation for vorticity. At each time step, the velocity is expressed via vorticity using a formula corresponding to the Biot-Savart-type law. We prove the first mean-square convergence order of the vorticity approximation.

• Journal Article Type: Article
• Acceptance Date: Aug 27, 2020
• Online Publication Date: Sep 14, 2020
• Publication Date: 2021
• Deposit Date: Sep 11, 2020
• Publicly Available Date: Sep 14, 2020
• Journal: NUMERICAL MATHEMATICS: Theory, Methods and Applications
• Peer Reviewed: Peer Reviewed
• Volume: 14
• Issue: 1
• Pages: 1-30
• DOI: https://doi.org/10.4208/nmtma.OA-2020-0034
• Keywords: Navier-Stokes equations; vorticity; numerical method; stochastic partial differential equa- tions; mean-square convergence
• Public URL: https://nottingham-repository.worktribe.com/output/4855421
• Publisher URL: http://www.global-sci.org/intro/online/read?article_id=967.html