Inviscid Limit for Stochastic Second-Grade Fluid Equations

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.

References in corpus (5)

• Vanishing Viscosity Limits and Boundary Layers for Circularly Symmetric 2D Flows
• Convergence of the 2D Euler-$\alpha$ to Euler equations in the Dirichlet case: indifference to boundary layers
• From additive to transport noise in 2D fluid dynamics
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Cited by in corpus (1)

• Dissipation properties of transport noise in the two-layer quasi-geostrophic model