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Related papers: Navier--Stokes equations in a curved thin domain

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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

We study the weak boundary layer phenomenon of the Navier-Stokes equations in a 3D bounded domain with viscosity, $\epsilon > 0$, under generalized Navier friction boundary conditions, in which we allow the friction coefficient to be a (1,…

Analysis of PDEs · Mathematics 2011-08-11 Gung-Min Gie , James P. Kelliher

In this paper, we investigate the vanishing viscosity limit for solutions to the Navier-Stokes equations with a Navier slip boundary condition on general compact and smooth domains in $\mathbf{R}^3$. We first obtain the higher order…

Analysis of PDEs · Mathematics 2015-06-03 Lizhen Wang , Zhouping Xin , Aibin Zang

We prove the existence of a weak solution to the three-dimensional steady compressible isentropic Navier-Stokes equations in bounded domains for any specific heat ratio \gamma > 1. Generally speaking, the proof is based on the new weighted…

Analysis of PDEs · Mathematics 2013-05-27 Song Jiang , Chunhui Zhou

In this paper, we study the three-dimensional axisymmetric compressible Navier-Stokes equations with slip boundary conditions in a cylindrical domain excluding the axis. We establish the global existence and exponential decay of weak,…

Analysis of PDEs · Mathematics 2025-11-19 Qinghao Lei

This paper is concerned with the existence and uniqueness of the strong solution to the incompressible Navier-Stokes equations with Navier-slip boundary conditions in a two-dimensional strip domain where the slip coefficients may not have…

Analysis of PDEs · Mathematics 2019-09-04 Quanrong Li , Shijin Ding

A proof of existence, uniqueness and smoothness of the Navier-Stokes equations is an actual problem, which solution is important for different branches of science. The subject of this study is obtaining the smooth and unique solutions of…

Fluid Dynamics · Physics 2016-08-30 Alexey V. Zhirkin

In this paper we investigate the issue of the inviscid limit for the compressible Navier-Stokes system in an impermeable fixed bounded domain. We consider two kinds of boundary conditions. The first one is the no-slip condition. In this…

Analysis of PDEs · Mathematics 2024-12-30 Franck Sueur

A mechanical model and finite element method for the simultaneous solution of Stokes and incompressible Navier-Stokes flows on multiple curved surfaces over a bulk domain are proposed. The two-dimensional surfaces are defined implicitly by…

Computational Engineering, Finance, and Science · Computer Science 2025-10-09 Michael Wolfgang Kaiser , Thomas-Peter Fries

In this article, we study the solutions of the damped Navier--Stokes equation with Navier boundary condition in a bounded domain $\Omega$ in $\mathbb{R}^3$ with smooth boundary. The existence of the solutions is global with the damped term…

Analysis of PDEs · Mathematics 2021-12-06 Rajib Haloi , Subha Pal

In this paper, we study the Navier-Stokes equations of compressible, barotropic flow posed in a bounded set in $\mathbb{R}^3$ with different boundary conditions. Specifically, we prove that the local-in-time smooth solution of the…

Analysis of PDEs · Mathematics 2020-11-24 Anthony Suen

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 [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 provide a rigorous derivation of the compressible Reynolds system as a singular limit of the compressible (barotropic) Navier-Stokes system on a thin domain. In particular, the existence of solutions to the Navier-Stokes system with…

Analysis of PDEs · Mathematics 2017-05-22 I. S. Ciuperca , E. Feireisl , M. Jai , A. Petrov

We show the existence of weak solutions to the fluid-structure interaction problem of a largely deforming viscoelastic bulk solid with a viscous fluid governed by the incompressible Navier-Stokes equations. In contrast to previous works,…

Analysis of PDEs · Mathematics 2026-03-13 Antonín Češík , Malte Kampschulte , Sebastian Schwarzacher

We study the motion of the steady compressible heat conducting viscous fluid in a bounded three dimensional domain governed by the compressible Navier-Stokes-Fourier system. Our main result is the existence of a weak solution to these…

Analysis of PDEs · Mathematics 2007-09-24 Piotr B. Mucha , Milan Pokorny

In this paper, we study the asymptotic behavior of solutions to the compressible Navier-Stokes system considered on a sequence of spatial domains, whose boundaries exhibit fast oscillations with amplitude and characteristic wave length…

This paper concerns the barotropic compressible Navier-Stokes equations in a two-dimensional half-space subject to Navier-slip boundary conditions with vacuum or non-vacuum far-field density. The global existence and large-time behavior of…

Analysis of PDEs · Mathematics 2026-05-29 Qinghao Lei , Weirong Liang

We consider the Navier-Stokes system describing the time evolution of a compressible barotropic fluid confined to a bounded spatial domain in the 3-D physical space, supplemented with the Navier's slip boundary conditions. It is shown that…

Analysis of PDEs · Mathematics 2014-04-08 Peter Bella , Eduard Feireisl , Bum Ja Jin , Antonin Novotny

We prove the inviscid limit for the incompressible Navier-Stokes equations for data that are analytic only near the boundary in a general two-dimensional bounded domain. Our proof is direct, using the vorticity formulation with a nonlocal…

Analysis of PDEs · Mathematics 2021-11-30 Claude Bardos , Trinh T. Nguyen , Toan T. Nguyen , Edriss S. Titi