Related papers: On Vanishing Viscosity with Inflow, Outflow
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…
The Navier-Stokes systems for compressible fluids with density-dependent viscosities are considered in the present paper. These equations, in particular, include the ones which are rigorously derived recently as the Saint-Venant system for…
We develop a mesh-based semi-Lagrangian discretization of the time-dependent incompressible Navier-Stokes equations with free boundary conditions recast as a non-linear transport problem for a momentum 1-form. A linearly implicit fully…
In the class of admissible weak solutions, we prove a weak-strong uniqueness result for the incompressible Euler equations assuming that the symmetric part of the gradient belongs to $L^1_{\rm loc}([0,+\infty);L^{\rm…
We prove that the Navier-Stokes equation is well-posed in function spaces on $\mathbb{R}^d$, $d\ge 2$, that contain vector fields of order $O(|x|^\kappa)$ as $|x|\to\infty$ with $\kappa<1/2$. The corresponding solutions depend continuously…
We study the behaviour of the solution $u_\varepsilon$ to the Navier-Stokes equations with vanishing viscosity and a non-slip condition in a randomly perforated domain. We consider the space $\mathbb{R}^3$ where we remove $N$ holes that are…
We study an inviscid limit problem for a class of Navier-Stokes equations with vanishing measurable viscous coefficients in 3-dimensional spatial domains whose boundaries are oscillatory, depending on a small parameter, and become flat when…
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…
The present paper is concerned with an inviscid limit problem of radially symmetric stationary solutions for an exterior problem in $\mathbb{R}^n (n\ge 2)$ to compressible Navier-Stokes equation, describing the motion of viscous barotropic…
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 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…
We analyze the two-dimensional incompressible Navier-Stokes equations on a smooth, bounded domain with Navier boundary conditions. Starting from an initial vorticity in $L^p$ with $p>2$, we show strong convergence of the vorticity in the…
In this paper, we consider the zero-viscosity limit of the Navier-Stokes equations in a half space with the Navier friction boundary condition $$ (\beta u^{\varepsilon}-\varepsilon^{\gamma}\partial_y u^{\varepsilon})|_{y=0}=0, $$ where…
In this paper, we study the zero-viscosity limit of the compressible Navier-Stokes equations in a half-space with non-slip boundary condition. We justify the Prandtl boundary layer expansion for the analytic data: the compressible…
This paper is concerned with the free boundary value problem for multi-dimensional Navier-Stokes equations with density-dependent viscosity where the flow density vanishes continuously across the free boundary. A local (in time) existence…
We consider the inviscid limit of the stochastic damped 2D Navier- Stokes equations. We prove that, when the viscosity vanishes, the stationary solution of the stochastic damped Navier-Stokes equations converges to a stationary solution of…
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…
In the vanishing viscosity limit from the Navier-Stokes to Euler equations on domains with boundaries, a main difficulty comes from the mismatch of boundary conditions and, consequently, the possible formation of a boundary layer. Within a…
The paper is concerned with the vanishing viscosity limit of the two-dimensional degenerate viscous lake equations when the Navier slip conditions are prescribed on the impermeable boundary of a simply connected bounded regular domain. When…
In this paper, we investigate the uniform regularity for the isentropic compressible Navier-Stokes system with general Navier-slip boundary conditions (1.6) and the inviscid limit to the compressible Euler system. It is shown that there…