Related papers: Inviscid Limit for Stochastic Second-Grade Fluid E…
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 Navier-Stokes equations with additive noise and no-slip boundary conditions to the solution…
In this paper, we consider the 2D second grade fluid past an obstacle satisfying the standard non-slip boundary condition at the surface of the obstacle. Second grade fluid model is a well-known non-Newtonian model, with two parameters:…
The second-grade fluid equations are a model for viscoelastic fluids, with two parameters: $\alpha > 0$, corresponding to the elastic response, and $\nu > 0$, corresponding to viscosity. Formally setting these parameters to $0$ reduces the…
We consider the convergence in the $L^2$ norm, uniformly in time, of the Navier-Stokes equations with Dirichlet boundary conditions to the Euler equations with slip boundary conditions. We prove that if the Oleinik conditions of no…
Chemin has shown that solutions of the Navier-Stokes equations in the plane for an incompressible fluid whose initial vorticity is bounded and lies in L^2 converge in the zero-viscosity limit in the L^2-norm to a solution of the Euler…
We consider stochastic Navier-Stokes equations in a 2D-bounded domain with the Navier with friction boundary condition. We establish the existence and the uniqueness of the solutions and study the vanishing viscosity limit. More precisely,…
The inviscid limit for the two-dimensional compressible viscoelastic equations on the half plane is considered under the no-slip boundary condition. When the initial deformation tensor is a perturbation of the identity matrix and the…
We study the limit of the stochastic model for two dimensional second grade fluids subjected to the periodic boundary conditions as the stress modulus tends to zero. We show that under suitable conditions on the data the whole sequence of…
We consider the flow of an { ideal} fluid in a 2D-bounded domain, admitting flows through the boundary of this domain. The flow is described by Euler equations with \textit{non-homogeneous } Navier slip boundary conditions. These conditions…
In this paper we investigate the issue of the inviscid limit for the compressible Navier-Stokes system in an impermeable fixed bounded domain. We consider two kinds of boundary conditions. The first one is the no-slip condition. In this…
We study the convergence rate of the solutions of the incompressible Euler-$\alpha$, an inviscid second-grade complex fluid, equations to the corresponding solutions of the Euler equations, as the regularization parameter $\alpha$…
We introduce an analogue to Kato's Criterion regarding the inviscid convergence of stochastic Navier-Stokes flows to the strong solution of the deterministic Euler equation. Our assumptions cover additive, multiplicative and transport type…
In the paper, the limit behavior of solutions to the second-grade fluid system with no-slip boundary conditions is studied as both $\nu$ and $\alpha$ tend to zero. More precisely, it is verified that the convergence from second-grade fluid…
We prove the existence and uniqueness of global, probabilistically strong, analytically strong solutions of the 2D Stochastic Navier-Stokes Equation under Navier boundary conditions. The choice of noise includes a large class of additive,…
This paper studies the inviscid limit problem for the two-dimensional Navier-Stokes equations with anisotropic viscosity. The fluid is assumed to be bounded above and below by impenetrable walls, with a no-slip boundary condition imposed on…
In [1], T. Clopeau, A. Mikeli\'c, and R. Robert studied the inviscid limit of the 2D incompressible Navier-Stokes equations in a bounded domain subject to Navier friction-type boundary conditions. They proved that the inviscid limit…
We prove that any weak space-time $L^2$ vanishing viscosity limit of a sequence of strong solutions of Navier-Stokes equations in a bounded domain of ${\mathbb{R}}^2$ satisfies the Euler equation if the solutions' local enstrophies are…
We consider the limit $\alpha\to0$ for a second grade fluid on a bounded domain with Dirichlet boundary conditions. We show convergence towards a solution of the Navier-Stokes equations under two different types of hypothesis on the initial…
We consider the vanishing viscosity limit of the Navier-Stokes equations in a half space, with Dirichlet boundary conditions. We prove that the inviscid limit holds in the energy norm if the product of the components of the Navier-Stokes…
We prove the existence and some moment estimates for an invariant measure $\mu$ for the two-dimensional ($2$D) deterministic Euler equations on the unbounded domain $\mathbb R^2$ and with highly regular initial data. The result is achieved…