English
Related papers

Related papers: Vanishing viscosity limit to vortex sheet for the …

200 papers

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

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 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

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

We say that the vanishing viscosity limit holds in the classical sense if the velocity for a solution to the Navier-Stokes equations converges in the energy norm uniformly in time to the velocity for a solution to the Euler equations. We…

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

This paper is a continuation of our previous work (arXiv:2507.03505), where the global existence and incompressible limit of weak solutions to the isentropic compressible Navier-Stokes equations in the half-plane with ripped density and…

Analysis of PDEs · Mathematics 2025-10-28 Shuai Wang , Guochun Wu , Xin Zhong

In this paper, we show the incompressible and vanishing vertical viscosity limits for the strong solutions to the isentropic compressible Navier-Stokes system with anistropic dissipation, in a domain with Dirichlet boundary conditions in…

Analysis of PDEs · Mathematics 2025-01-10 Nader Masmoudi , Changzhen Sun , Chao Wang , Zhifei Zhang

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

We are concerned with the inviscid limit of the Navier-Stokes equations to the Euler equations for barotropic compressible fluids in $\mathbb{R}^3$. When the viscosity coefficients obey a lower power-law of the density (i.e., $\rho^\delta$…

Analysis of PDEs · Mathematics 2021-12-21 Geng Chen , Gui-Qiang G. Chen , Shengguo Zhu

In this paper, we consider the inviscid limit of the incompressible Navier-Stokes equations in a smooth, bounded and simply connected domain $\Omega \subset \mathbb{R}^d, d=2,3$. We prove that for a vortex patch initial data the weak Leray…

Analysis of PDEs · Mathematics 2010-04-26 Quansen Jiu , Yun Wang

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 obtain existence and conormal Sobolev regularity of strong solutions to the 3D compressible isentropic Navier-Stokes system on the half-space with a Navier boundary condition, over a time that is uniform with respect to the viscosity…

Analysis of PDEs · Mathematics 2014-10-13 Matthew Paddick

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

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

This paper concerns the low Mach number limit of weak solutions to the compressible Navier-Stokes equations for isentropic fluids in a bounded domain with a Navier-slip boundary condition. In \cite{DGLM99}, it has been proved that if the…

Analysis of PDEs · Mathematics 2017-05-04 Xiong Linjie

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 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

Chemin has shown that solutions of the Navier-Stokes equations in the plane for an incompressible fluid whose initial vorticity is bounded and lies in L^2 converge in the zero-viscosity limit in the L^2-norm to a solution of the Euler…

Mathematical Physics · Physics 2007-05-23 James P. Kelliher

In the recent paper, the global-in-time inviscid limit of the three-dimensional (3D) isentropic compressible Navier-Stokes equations is considered. First, when viscosity coefficients are given as a constant multiple of density's power…

Analysis of PDEs · Mathematics 2019-11-21 Yongcai Geng , Yachun Li , Shengguo Zhu