Related papers: Boundary layer analysis of the Navier-Stokes equat…
In this paper, we investigate the vanishing viscosity limit for solutions to the Navier-Stokes equations with a Navier slip boundary condition on general compact and smooth domains in $\mathbf{R}^3$. We first obtain the higher order…
In this paper, we investigate the vanishing viscosity limit problem for the 3-dimensional (3D) incompressible Navier-Stokes equations in a general bounded smooth domain of $R^3$ with the generalized Navier-slip boundary conditions…
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…
In this paper, we establish vanishing viscosity limit of the 2D Navier-Stokes equations in a horizontally periodic strip. On the vertical direction, the horizontal component of the velocity is subjected to two different types of boundary…
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…
In this paper, we study the inviscid limit of the free surface incompressible Navier-Stokes equations with or without surface tension. By delicate estimates, we prove the weak boundary layer of the velocity of the free surface Navier-Stokes…
We consider solutions to the Navier-Stokes equations with Navier boundary conditions in a bounded domain in the plane with a C^2-boundary. Navier boundary conditions can be expressed in the form w = (2 K - A) v . T and v . n = 0 on the…
In this paper we study the vanishing viscosity limit for the inhomogeneous incompressible Navier-Stokes equations on bounded domains with no-slip boundary condition in two or three space dimensions. We show that, under suitable assumptions…
We study the high Reynolds number limit of a viscous fluid in the presence of a rough boundary. We consider the two-dimensional incompressible Navier-Stokes equations with Navier slip boundary condition, in a domain whose boundaries exhibit…
In this paper, we investigate the uniform regularity of solutions to the 3-dimensional isentropic compressible Navier-Stokes system with free surfaces and study the corresponding asymptotic limits of such solutions to that of the…
We address the issue of existence of weak solutions for the non-homogeneous Navier-Stokes system with Navier friction boundary conditions allowing the presence of vacuum zones and assuming rough conditions on the data. We also study the…
We consider the problem of the strong convergence, as the viscosity goes to zero, of the solutions to the three-dimensional evolutionary Navier-Stokes equations under a Navier slip-type boundary condition to the solution of the Euler…
We study the three-dimensional incompressible Navier-Stokes equations in a smooth bounded domain $\Omega$ with initial velocity $u_0$ square-integrable, divergence-free and tangent to $\partial \Omega$. We supplement the equations with the…
In this paper, we study the vanishing viscosity limit for a coupled Navier-Stokes/Allen-Cahn system in a bounded domain. We first show the local existence of smooth solutions of the Euler/Allen-Cahn equations by modified Galerkin method.…
We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in $\R^n$ with compact and smooth boundary, subject to the kinematic and vorticity boundary conditions on the non-flat…
We study the zero-viscosity limit of free boundary Navier-Stokes equations with surface tension in $\mathbb{R}^3$ thus extending the work of Masmoudi and Rousset [1] to take surface tension into account. Due to the presence of boundary…
The focus of this paper is on the analysis of the boundary layer and the associated vanishing viscosity limit for two classes of flows with symmetry, namely, Plane-Parallel Channel Flows and Parallel Pipe Flows. We construct explicit…
Consider the steady solution to the incompressible Euler equation $\bar u=Ae_1$ in the periodic tunnel $\Omega=\mathbb T^{d-1}\times(0,1)$ in dimension $d=2,3$. Consider now the family of solutions $u^\nu$ to the associated Navier-Stokes…
In this paper we study the Navier-Stokes equations with a Navier-type boundary condition that has been proposed as an alternative to common near wall models. The boundary condition we study, involving a linear relation between the…
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,…