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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

The global well-posedness and inviscid limit are investigated for the fluid-particle interaction system, described by the Navier-Stokes equations for the inhomogeneous incompressible viscous flows coupled with the Vlasov-Fokker-Planck…

Analysis of PDEs · Mathematics 2025-12-15 Fucai Li , Jinkai Ni , Ling-Yun Shou , Dehua Wang

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

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 uniform bounds and the inviscid limit in $L^p$-based Sobolev conormal spaces for the solutions of the Navier-Stokes equations with the Navier boundary conditions in the half-space. We extend the vanishing viscosity results…

Analysis of PDEs · Mathematics 2025-02-07 Mustafa Sencer Aydın

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

The 2D Euler system, which governs inviscid incompressible fluid flow, can admit infinitely many steady solutions in a given domain with slip boundary conditions. To select physical classical solutions, we investigate the vanishing…

Analysis of PDEs · Mathematics 2026-05-21 Changfeng Gui , Chunjing Xie , Huan Xu

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

In this paper we study the vanishing viscosity limit for the inhomogeneous incompressible Navier-Stokes equations on bounded domains with no-slip boundary condition in two or three space dimensions. We show that, under suitable assumptions…

Analysis of PDEs · Mathematics 2025-07-03 Jens Schröder , Emil Wiedemann

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

It is challenging to perform a multiscale analysis of mesoscopic systems exhibiting singularities at the macroscopic scale. In this paper, we study the hydrodynamic limit of the Boltzmann equations $$\mathrm{St} \partial_t F + v\cdot…

Analysis of PDEs · Mathematics 2022-06-02 Chanwoo Kim , Joonhyun La

We establish the inviscid limit of the incompressible Navier-Stokes equations on the whole plane $\mathbb{R}^2$ for initial data having vorticity as a superposition of point vortices and a regular component. In particular, this rigorously…

Analysis of PDEs · Mathematics 2019-02-22 Toan T. Nguyen , Trinh T. Nguyen

We consider the inviscid limit for the two-dimensional incompressible Navier-Stokes equation in the particular case where the initial flow is a finite collection of point vortices. We suppose that the initial positions and the circulations…

Analysis of PDEs · Mathematics 2015-05-13 Thierry Gallay

We show that, in general, the solutions to the initial-boundary value problem for the Navier-Stokes equations under a widely adopted Navier-type slip boundary condition do not converge, as the viscosity goes to zero (in any arbitrarily…

Analysis of PDEs · Mathematics 2010-10-26 H. Beirão da Veiga , F. Crispo

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

For periodic initial data with the density allowing vacuum, we establish the global existence and exponential decay of weak, strong and classical solutions to the two-dimensional(2D) compressible Navier-Stokes equations when the bulk…

Analysis of PDEs · Mathematics 2025-07-03 Qinghao Lei , Chengfeng Xiong

This paper studies the inviscid limit problem for the two-dimensional Navier-Stokes equations with anisotropic viscosity. The fluid is assumed to be bounded above and below by impenetrable walls, with a no-slip boundary condition imposed on…

Analysis of PDEs · Mathematics 2025-07-04 Chongsheng Cao , Yanqiu Guo

IIn the paper, we consider the inviscid, incompressible and semiclassical limits limits of the barotropic quantum Navier-Stokes equations of compressible flows in a periodic domain. We show that the limit solutions satisfy the…

Analysis of PDEs · Mathematics 2018-07-19 Hongli Wang , Jianwei Yang

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