Inviscid Limit for Stochastic Second-Grade Fluid Equations
- Authors: Eliseo Luongo
- Preprint year: 2022
- First public date: 2022-07-07
- arXiv: 2207.03174
- Status: Published
- Publication type: Journal article
- Publication year: 2024
- Published online: 2023-06-29
- Journal: Stochastics and Partial Differential Equations: Analysis and Computations 12(2), 1046–1099 (2024)
- DOI: 10.1007/s40072-023-00303-y
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 second-grade fluid equations with transport noise and no-slip boundary conditions to the solution of the corresponding Euler equations. We prove, that assuming proper regularity of the initial conditions of the Euler equations and a proper behavior of the parameters $\nu$ and $\alpha$, then the inviscid limit holds without requiring a particular dissipation of the energy of the solutions of the second-grade fluid equations in the boundary layer.