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Related papers: Observations on the vanishing viscosity limit

200 papers

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 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

In a three-dimensional bounded domain $\Omega$ we consider the compressible Navier-Stokes equations for a barotropic fluid with general non-linear density dependent viscosities and no-slip boundary conditions. A nonlinear drag term is added…

Analysis of PDEs · Mathematics 2025-02-11 Luca Bisconti , Matteo Caggio , Filippo Dell'Oro

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 consider the Euler system of gas dynamics endowed with the incomplete equation of state relating the internal energy to the mass density and the pressure. We show that any sufficiently smooth solution can be recovered as a vanishing…

Analysis of PDEs · Mathematics 2022-06-22 Eduard Feireisl , Christian Klingenberg , Simon Markfelder

$(-1)$-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

We study the inviscid limit of the free boundary Navier-Stokes equations. We prove the existence of solutions on a uniform time interval by using a suitable functional framework based on Sobolev conormal spaces. This allows us to use a…

Analysis of PDEs · Mathematics 2012-02-06 Nader Masmoudi , Frédéric Rousset

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 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 consider solutions to the Navier-Stokes equations with Navier boundary conditions in a bounded domain in the plane with a C^2-boundary. Navier boundary conditions can be expressed in the form w = (2 K - A) v . T and v . n = 0 on the…

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

In this paper we consider the vanishing viscosity limit of solutions to the initial boundary value problem for compressible viscoelastic equations in the half space. When the initial deformation gradient does not degenerate and there is no…

Analysis of PDEs · Mathematics 2023-07-18 Xumin Gu , Dehua Wang , Feng Xie

In [Lacave, IHP, ana, to appear (2008)] the author considered the two dimensional Euler equations in the exterior of a thin obstacle shrinking to a curve and determined the limit velocity. In the present work, we consider the same problem…

Analysis of PDEs · Mathematics 2009-02-13 Christophe Lacave

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

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 study the zero-viscosity limit of the compressible Navier-Stokes equations in a half-space with non-slip boundary condition. We justify the Prandtl boundary layer expansion for the analytic data: the compressible…

Analysis of PDEs · Mathematics 2023-05-17 Chao Wang , Yuxi Wang , Zhifei Zhang

Consider the dynamics of a layer of viscous incompressible fluid under the influence of gravity. The upper boundary is a free boundary with the effect of surface tension taken into account, and the lower boundary is a fixed boundary on…

Analysis of PDEs · Mathematics 2019-11-12 Yanjin Wang , Zhouping Xin

We consider the free boundary problem of compressible isentropic neo-Hookean viscoelastic fluid equations with surface tension. Under the physical kinetic and dynamic conditions proposed on the free boundary, we investigate regularities of…

Analysis of PDEs · Mathematics 2022-01-19 Xumin Gu , Yu Mei

The quasi-neutral limit of the Navier-Stokes-Poisson system modeling a viscous plasma with vanishing viscosity coefficients in the half-space $\mathbb{R}^{3}_{+}$ is rigorously proved under a Navier-slip boundary condition for velocity and…

Analysis of PDEs · Mathematics 2022-07-19 Qiangchang Ju , Tao Luo , Xin Xu

We construct global weak solutions of the Euler equations in an infinite cylinder $\Pi=\{x\in \mathbb{R}^{3}\ |\ x_h=(x_1,x_2),\ r=|x_h|<1\}$ for axisymmetric initial data without swirl when initial vorticity…

Analysis of PDEs · Mathematics 2019-01-08 Ken Abe

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