Inviscid limit for Stochastic Navier-Stokes Equations under general initial conditions
- Authors: Eliseo Luongo
- Preprint year: 2021
- First public date: 2021-11-28
- arXiv: 2111.14189
- Status: Published
- Publication type: Journal article
- Publication year: 2024
- Journal: Journal of Differential Equations 389, 114–149 (2024)
- DOI: 10.1016/j.jde.2024.01.010
Abstract
We consider in a smooth and bounded two dimensional domain the convergence in the $L^2$ norm, uniformly in time, of the solution of the stochastic Navier-Stokes equations with additive noise and no-slip boundary conditions to the solution of the corresponding Euler equations. We prove, under general regularity on the initial conditions of the Euler equations, that assuming the dissipation of the energy of the solution of the Navier-Stokes equations in a Kato type boundary layer, then the inviscid limit holds.