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Related papers: On the vanishing viscosity limit in a disk

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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…

Analysis of PDEs · Mathematics 2024-04-30 Mingwen Fei , Xinghong Pan , Jianfeng Zhao

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…

Analysis of PDEs · Mathematics 2017-12-06 Peter Constantin , Vlad Vicol

We consider the flow of a viscous, incompressible, Newtonian fluid in a perforated domain in the plane. The domain is the exterior of a regular lattice of rigid particles. We study the simultaneous limit of vanishing particle size and…

Analysis of PDEs · Mathematics 2015-08-31 Christophe Lacave , Anna Mazzucato

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

The validity of the vanishing viscosity limit, that is, whether solutions of the Navier-Stokes equations modeling viscous incompressible flows converge to solutions of the Euler equations modeling inviscid incompressible flows as viscosity…

Analysis of PDEs · Mathematics 2016-10-19 Yasunori Maekawa , Anna Mazzucato

$(-1)$-homogeneous axisymmetric no-swirl solutions of three dimensional incompressible stationary Navier-Stokes equations which are smooth on the unit sphere minus the north and south poles have been classified, %as a four parameter family…

Analysis of PDEs · Mathematics 2019-05-31 Li Li , Yan Yan Li , Xukai Yan

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

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…

Analysis of PDEs · Mathematics 2026-04-17 Richard M. Höfer , Eleni Hübner-Rosenau

We consider the inviscid limit for the two-dimensional Navier--Stokes equations in the class of integrable and bounded vorticity fields. It is expected that the difference between the Navier--Stokes and Euler velocity fields vanishes in…

Analysis of PDEs · Mathematics 2021-07-01 Christian Seis

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 inviscid limit problem to the higher dimensional incompressible Navier--Stokes equations in the whole space. It is shown in [Guo, Li, Yin: J. Funct. Anal., 276 (2019)] that given initial data $u_0\in…

Analysis of PDEs · Mathematics 2023-06-06 Jinlu Li , Yanghai Yu , Weipeng Zhu

In this paper, we study the vanishing viscosity of the isentropic compressible Navier-Stokes equations with density dependent viscous coefficient in the presence of the shock wave. Given a shock wave to the corresponding Euler equations, we…

Analysis of PDEs · Mathematics 2019-05-16 Meiying Cui

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 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

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 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 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 consider the motion of a compressible, viscous, and heat conducting fluid in the regime of small viscosity and heat conductivity. It is shown that weak solutions of the associated Navier- Stokes-Fourier system converge to a (strong)…

Analysis of PDEs · Mathematics 2015-06-09 Eduard Feireisl

We prove the existence of relative finite-energy vanishing viscosity solutions of the one-dimensional, isentropic Euler equations under the assumption of an asymptotically isothermal pressure law, that is, $p(\rho)/\rho = O(1)$ in the limit…

Analysis of PDEs · Mathematics 2020-06-08 Matthew R. I. Schrecker , Simon Schulz

In the present paper, we study the uniform regularity and vanishing dissipation limit for the full compressible Navier-Stokes system whose viscosity and heat conductivity are allowed to vanish at different order. The problem is studied in a…

Analysis of PDEs · Mathematics 2015-08-18 Wang Yong