Inviscid limit for stochastic second-grade fluid equations

We consider in a smooth bounded and simply connected 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 ? and a, 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.

Automated summary

We study the convergence 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 in a smooth bounded and simply connected two dimensional domain. We prove that, under proper regularity of the initial conditions of the Euler equations and appropriate behavior of the parameters ? and a, the inviscid limit holds without requiring specific dissipation of the energy of the solutions in the boundary layer.