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We investigate the existence and the zero viscosity limit of steady compressible shear flow with Navier-slip boundary condition in the absence of any external force in a two-dimension domain $\Omega=(0,L)\times(0,2)$. More precisely, under…

Analysis of PDEs · Mathematics 2024-06-10 Wenbin Li , Chunhui Zhou

In this article we consider viscous flow in the exterior of an obstacle satisfying the standard no-slip boundary condition at the surface of the obstacle. We seek conditions under which solutions of the Navier-Stokes system in the exterior…

Analysis of PDEs · Mathematics 2009-02-17 D. Iftimie , M. C. Lopes Filho , H. J. Nussenzveig Lopes

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…

Analysis of PDEs · Mathematics 2023-08-30 Alexis F. Vasseur , Jincheng Yang

Assuming that initial velocity has finite energy and initial vorticity is bounded in the plane, we show that for any finite time interval the unique solutions of the Navier-Stokes equations converge uniformly to the unique solution of the…

Analysis of PDEs · Mathematics 2009-03-27 Elaine Cozzi

We establish convergence as the viscosity vanishes of solutions of the Navier-Stokes equations to a solution of the Euler equations for inflow, outflow boundary conditions. We extend the approach of Temam and Wang 2002, allowing the…

Analysis of PDEs · Mathematics 2025-06-24 Michael A. Gulas , James P. Kelliher

This paper is concerned with the vanishing dissipation limiting problem of one-dimensional non-isentropic Navier-Stokes equations with shock data. The limiting problem was solved in 1989 by Hoff-Liu in [13] for isentropic gas with single…

Analysis of PDEs · Mathematics 2024-05-30 Feimin Huang , Teng Wang

There are a few examples of solutions to the incompressible Euler equations which are piecewise smooth with a discontinuity of the tangential velocity across a hypersurface evolving in time: the so-called vortex sheets. An important open…

Analysis of PDEs · Mathematics 2017-08-30 Franck Sueur

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…

Analysis of PDEs · Mathematics 2013-01-07 Yuelong Xiao , Zhouping Xin

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.…

Analysis of PDEs · Mathematics 2011-10-26 Liyun Zhao , Boling Guo , Haiyang Huang

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…

Analysis of PDEs · Mathematics 2017-06-23 David Gérard-Varet , Christophe Lacave , Toan T. Nguyen , Frédéric Rousset

In this paper, we consider the small viscosity limit problem for the isentropic compressible Navier-Stokes equations in a 2D exterior domain with impermeable boundary conditions , and the corresponding Euler equations have vortex sheet…

Analysis of PDEs · Mathematics 2019-06-26 Helong Lu

Assuming that initial velocity and initial vorticity are bounded in the plane, we show that on a sufficiently short time interval the unique solutions of the Navier-Stokes equations converge uniformly to the unique solution of the Euler…

Analysis of PDEs · Mathematics 2008-08-27 Elaine Cozzi

We prove the convergence of the vanishing viscosity limit of the one-dimensional, isentropic, compressible Navier-Stokes equations to the isentropic Euler equations in the case of a general pressure law. Our strategy relies on the…

Analysis of PDEs · Mathematics 2018-10-18 Matthew R. I. Schrecker , Simon Schulz

We consider the incompressible Navier-Stokes and Euler equations in a bounded domain with non-characteristic boundary condition, and study the energy dissipation near the outflow boundary in the zero-viscosity limit. We show that in a…

Analysis of PDEs · Mathematics 2025-06-17 Jincheng Yang , Vincent R. Martinez , Anna L. Mazzucato , Alexis F. Vasseur

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…

Analysis of PDEs · Mathematics 2015-01-09 Wang Yong , Xin Zhouping , Yong Yan

We study the weak boundary layer phenomenon of the Navier-Stokes equations in a 3D bounded domain with viscosity, $\epsilon > 0$, under generalized Navier friction boundary conditions, in which we allow the friction coefficient to be a (1,…

Analysis of PDEs · Mathematics 2011-08-11 Gung-Min Gie , James P. Kelliher

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…

We study the vanishing viscosity limit for the incompressible Navier-Stokes equations (NSE) in a general bounded domain with inflow-outflow boundary conditions. Extending the work of Gie, Hamouda, and Temam ( Netw. Heterog. Media 7, 2012)…

Analysis of PDEs · Mathematics 2025-10-02 Anna L. Mazzucato , Dehua Wang , Wei Wei

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…

Analysis of PDEs · Mathematics 2025-11-07 Josef Demmel , Emil Wiedemann

We establish the global existence of weak solutions to the isentropic compressible Navier-Stokes equations in three-dimensional annular cylinders with Navier-slip boundary conditions, allowing large axisymmetric initial data and vacuum…

Analysis of PDEs · Mathematics 2026-05-11 Shuai Wang , Guochun Wu , Xin Zhong