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We show strong convergence of the vorticities in the vanishing viscosity limit for the incompressible Navier-Stokes equations on the two-dimensional torus, assuming only that the initial vorticity of the limiting Euler equations is in $L^p$…

Analysis of PDEs · Mathematics 2021-07-07 Helena J. Nussenzveig Lopes , Christian Seis , Emil Wiedemann

In this paper, we investigate the vanishing viscosity limit for the 3D nonhomogeneous incompressible Navier-Stokes equations with a slip boundary condition. We establish the local well-posedness of the strong solutions for initial boundary…

Analysis of PDEs · Mathematics 2017-11-22 Pengfei Chen , Yuelong Xiao , Hui Zhang

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

The aim of this contribution is to make a connection between two recent results concerning the dynamics of vortices in incompressible planar flows. The first one is an asymptotic expansion, in the vanishing viscosity limit, of the solution…

Analysis of PDEs · Mathematics 2012-12-10 Thierry Gallay

We continue the work of Lopes Filho, Mazzucato and Nussenzveig Lopes [LMN], on the vanishing viscosity limit of circularly symmetric viscous flow in a disk with rotating boundary, shown there to converge to the inviscid limit in $L^2$-norm…

Analysis of PDEs · Mathematics 2009-02-17 M. C. Lopes Filho , A. L. Mazzucato , H. J. Nussenzveig Lopes , Michael Taylor

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…

Analysis of PDEs · Mathematics 2015-06-11 Milton C. Lopes Filho , Helena J. Nussenzveig Lopes , Edriss S. Titi , Aibin Zang

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…

Probability · Mathematics 2023-08-16 Daniel Goodair , Dan Crisan

In this paper, we establish the vanishing viscosity limit result of the 2D stationary Navier-Stokes equations outside a rotating disc. On the boundary of the disc, the fluid is subjected to a small perturbation of a non zero rotation of…

Analysis of PDEs · Mathematics 2025-11-26 Xinghong Pan , Jianfeng Zhao

The vanishing viscosity limit of the two-dimensional (2D) compressible isentropic Navier-Stokes equations is studied in the case that the corresponding 2D inviscid Euler equations admit a planar rarefaction wave solution. It is proved that…

Analysis of PDEs · Mathematics 2019-10-23 Lin-An Li , Dehua Wang , Yi Wang

We construct global weak solutions of the Euler equations in an infinite cylinder $\Pi=\{x\in \mathbb{R}^{3}\ |\ x_h=(x_1,x_2),\ r=|x_h|<1\}$ for axisymmetric initial data without swirl when initial vorticity…

Analysis of PDEs · Mathematics 2019-01-08 Ken Abe

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

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 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…

Analysis of PDEs · Mathematics 2024-09-25 N. V. Chemetov , S. N. Antontsev

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

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 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,…

Probability · Mathematics 2014-05-05 Fernanda Cipriano , Iván Torrecilla

The quasi-neutral limit of the Navier-Stokes-Poisson system modeling a viscous plasma with vanishing viscosity coefficients in the half-space $\mathbb{R}^{3}_{+}$ is rigorously proved under a Navier-slip boundary condition for velocity and…

Analysis of PDEs · Mathematics 2022-07-19 Qiangchang Ju , Tao Luo , Xin Xu

Fluid flows around a symmetric obstacle generate vortices which may lead to symmetry breaking of the streamlines. We study this phenomenon for planar viscous flows governed by the stationary Navier-Stokes equations with constant…

Analysis of PDEs · Mathematics 2021-12-30 Filippo Gazzola , Gianmarco Sperone , Tobias Weth

We consider a sequence of Leray-Hopf weak solutions of the 2D Navier-Stokes equations on a bounded domain, in the vanishing viscosity limit. We provide sufficient conditions on the associated vorticity measures, away from the boundary,…

Analysis of PDEs · Mathematics 2019-06-26 Peter Constantin , Milton Lopes Filho , Helena Nussenzveig Lopes , Vlad Vicol

We say that the solution u to the Navier-Stokes equations converges to a solution v to the Euler equations in the vanishing viscosity limit if u converges to v in the energy norm uniformly over a finite time interval. Working specifically…

Mathematical Physics · Physics 2009-03-18 James P Kelliher