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.File in questo prodotto:
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Inviscid_SG.pdf
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Inviscid_limit_for_stochastic_2023.pdf
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