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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

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

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

We study a singular limit for the compressible Navier-Stokes system when the Mach and Rossby numbers are proportional to certain powers of a small parameter $\ep$. If the Rossby number dominates the Mach number, the limit problem is…

Analysis of PDEs · Mathematics 2015-05-27 Eduard Feireisl , Isabelle Gallagher , David Gérard-Varet , Antonin Novotny

We consider the compressible Navier-Stokes system describing the motion of a viscous fluid confined to a straight layer $\Omega_{\delta}=(0,\delta)\times\mathbb{R}^2$. We show that the weak solutions in the 3D domain converge strongly to…

Analysis of PDEs · Mathematics 2020-01-29 Matteo Caggio , Donatella Donatelli , Sarka Necasova , Yongzhong Sun

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 study singular limit for scaled barotropic Euler system modelling a rotating, compressible and inviscid fluid, where Mach and Rossby numbers are proportional to a small parameter $\epsilon$. If the fluid is confined to an infinite slab,…

Analysis of PDEs · Mathematics 2019-07-17 Nilasis Chaudhuri

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 article we consider viscous flow in the exterior of an obstacle satisfying the standard no-slip boundary condition at the surface of the obstacle. We seek conditions under which solutions of the Navier-Stokes system in the exterior…

Analysis of PDEs · Mathematics 2009-02-17 D. Iftimie , M. C. Lopes Filho , H. J. Nussenzveig Lopes

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

The compressible barotropic Navier-Stokes type system in monodimensional case with Neumann boundary condition given on free boundary is considered. The local and the global existence with uniformly boundedness for small viscosity…

Classical Analysis and ODEs · Mathematics 2009-09-09 Ewelina Kaminska

In this paper we consider the Navier-Stokes-Korteweg equations for a viscous compressible fluid with capillarity effects in three space dimensions. We prove global existence of finite energy weak solutions for large initial data. Contrary…

Analysis of PDEs · Mathematics 2019-03-07 Paolo Antonelli , Stefano Spirito

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

This paper investigates the Cauchy problem for the barotropic compressible Navier-Stokes equations in $\mathbb{R}^2$ with the constant state as far field, which may be vacuum or non-vacuum. Under the assumption of a sufficiently large bulk…

Analysis of PDEs · Mathematics 2026-01-27 Qinghao Lei , Chengfeng Xiong

We investigate the high viscosity limit (also called inertial limit) of the barotropic compressible Navier-Stokes equations supplemented with initial data which are perturbations of a stable constant solution. In the case of constant…

Analysis of PDEs · Mathematics 2026-03-17 Raphaël Danchin

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 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

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

This paper studies the inviscid limit of the two-dimensional incompressible viscoelasticity, which is a system coupling a Navier-Stokes equation with a transport equation for the deformation tensor. The existence of global smooth solutions…

Analysis of PDEs · Mathematics 2019-07-11 Yuan Cai , Zhen Lei , Fanghua Lin , Nader Masmoudi

We are concerned with the inviscid limit of the Navier-Stokes equations to the Euler equations for compressible fluids in $\mathbb{R}^3$. Motivated by the Kolmogorov hypothesis (1941) for incompressible flow, we introduce a Kolmogorov-type…

Analysis of PDEs · Mathematics 2019-10-02 Gui-Qiang G. Chen , James Glimm