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Related papers: Observations on the vanishing viscosity limit

200 papers

We establish the vanishing viscosity limit of the Navier-Stokes equations to the Euler equations for three-dimensional compressible isentropic flow in the whole space. It is shown that there exists a unique regular solution of compressible…

Analysis of PDEs · Mathematics 2019-06-26 Yongcai Geng , Yachun Li , Shengguo Zhu

In this paper, we study the vanishing viscosity limit of one-dimensional isentropic compressible Navier-Stokes equations with density-dependent viscosity, to the isentropic compressible Euler equations. Based on several new uniform…

Analysis of PDEs · Mathematics 2010-09-22 Feimin Huang , Ronghua Pan , Tianyi Wang , Yong Wang , Xiaoyun Zhai

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 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

We establish the vanishing viscosity limit of the Navier-Stokes equations to the isentropic Euler equations for one-dimensional compressible fluid flow. For the Navier-Stokes equations, there exist no natural invariant regions for the…

Analysis of PDEs · Mathematics 2009-10-14 Gui-Qiang Chen , Mikhail Perepelitsa

We study the vanishing viscosity limit for the three-dimensional incompressible Navier-Stokes equations in terms of the relative vorticity in the setting of axisymmetric velocity fields without swirl. We show that the weak convergence of…

Analysis of PDEs · Mathematics 2023-03-06 Patrick Brkic , Emil Wiedemann

We address the inviscid limit for the Navier-Stokes equations in a half space, with initial datum that is analytic only close to the boundary of the domain, and has finite Sobolev regularity in the complement. We prove that for such data…

Analysis of PDEs · Mathematics 2019-04-12 Igor Kukavica , Vlad Vicol , Fei Wang

We prove that there exists an interval of time which is uniform in the vanishing viscosity limit and for which the Navier-Stokes equation with Navier boundary condition has a strong solution. This solution is uniformly bounded in a conormal…

Analysis of PDEs · Mathematics 2015-05-19 Nader Masmoudi , Frederic Rousset

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 zero viscosity limit of the incompressible Navier-Stokes equations with non-slip boundary condition in the half-space for the initial vorticity located away from the boundary. By using the vorticity formulation and…

Analysis of PDEs · Mathematics 2016-09-14 Mingwen Fei , Tao Tao , Zhifei Zhang

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

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

This is the second of two papers devoted to the asymptotic behavior of solutions to the incompressible Navier-Stokes equations in a half-space with point vortex initial data. A major difficulty stems from the interaction between the point…

Analysis of PDEs · Mathematics 2026-04-08 Chao Wang , Jingchao Yue , Zhifei Zhang

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…

Analysis of PDEs · Mathematics 2025-03-11 Tuoc Phan , Dario A. Valdebenito

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…

Analysis of PDEs · Mathematics 2025-08-05 Christian Seis , Emil Wiedemann , Jakub Woźnicki

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

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…

Analysis of PDEs · Mathematics 2015-05-28 Quansen Jiu , Dongjuan Niu , Jiahong Wu

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 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…

Analysis of PDEs · Mathematics 2014-04-01 Peter Constantin , Igor Kukavica , Vlad Vicol

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