Global well-posedness of 2D Navier-Stokes with Dirichlet boundary fractional noise
- Authors: Antonio Agresti, Alexandra Blessing, Eliseo Luongo
- First public date: 2024-07-04
- arXiv: 2407.03988
- Preprint year: 2024
- Status: Published
- Publication type: Journal article
- Publication year: 2025
- Journal: Nonlinearity 38, 075023 (2025)
- DOI: 10.1088/1361-6544/ade21c
Abstract
In this paper, we prove the global well-posedness and interior regularity for the 2D Navier-Stokes equations driven by a fractional noise acting as an inhomogeneous Dirichlet-type boundary condition. The model describes a vertical slice of the ocean with a relative motion between the two surfaces and can be thought of as a stochastic variant of the Couette flow. The relative motion of the surfaces is modeled by a Gaussian noise which is coloured in space and fractional in time with Hurst parameter greater than 3/4.