We consider in a smooth bounded and simply connected two dimensional domain the convergence in the L2 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 ν and α, 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.

Inviscid limit for stochastic second-grade fluid equations

Luongo, Eliseo
2024

Abstract

We consider in a smooth bounded and simply connected two dimensional domain the convergence in the L2 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 ν and α, 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.
2024
Settore MAT/06 - Probabilita' e Statistica Matematica
Additive noise; boundary layer; inviscid limit; no-slip boundary conditions; second-grade complex fluid; transport noise; turbulence; zero viscosity limit; euler equations; boundary; space
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/142287
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