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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

Assuming that initial velocity has finite energy and initial vorticity is bounded in the plane, we show that for any finite time interval the unique solutions of the Navier-Stokes equations converge uniformly to the unique solution of the…

Analysis of PDEs · Mathematics 2009-03-27 Elaine Cozzi

We establish the existence of a uniformly bounded $ C^\infty $ solution of the Navier-Stokes equations on $\mathbb{R}^3 x\ [0, \infty) $ without external forces or boundaries for a divergence free initial condition $ u_o \in \cap_m H^m $…

General Mathematics · Mathematics 2025-03-25 Gray Jennings

We propose a finite element discretization for the steady, generalized Navier-Stokes equations for fluids with shear-dependent viscosity, completed with inhomogeneous Dirichlet boundary conditions and an inhomogeneous divergence constraint.…

Numerical Analysis · Mathematics 2023-10-09 Julius Jeßberger , Alex Kaltenbach

This paper exposes how to obtain a relation that have to be hold for all free--divergence velocity fields that evolve according to Navier--Stokes equations. However, checking the violation of this relation requires a huge computational…

Fluid Dynamics · Physics 2019-08-06 Manuel García-Casado

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

In this paper, we study the problem concerning the approximation of a rigid obstacle for flows governed by the stationary Navier-Stokes equations in the two-dimensional case. The idea is to consider a highly viscous fluid in the place of…

Analysis of PDEs · Mathematics 2022-09-26 Sadokat Malikova

We address the inviscid limit for the Navier-Stokes equations in a half space, with initial datum that is analytic only close to the boundary of the domain, and has finite Sobolev regularity in the complement. We prove that for such data…

Analysis of PDEs · Mathematics 2019-04-12 Igor Kukavica , Vlad Vicol , Fei Wang

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

We study the three-dimensional incompressible Navier-Stokes equations in a smooth bounded domain $\Omega$ with initial velocity $u_0$ square-integrable, divergence-free and tangent to $\partial \Omega$. We supplement the equations with the…

Loosely speaking, the Navier-Stokes-$\alpha$ model and the Navier-Stokes equations differ by a spatial filtration parametrized by a scale denoted $\alpha$. Starting from a strong two-dimensional solution to the Navier-Stokes-$\alpha$ model…

Analysis of PDEs · Mathematics 2022-10-06 Jad Doghman , Ludovic Goudenège

The steady motion of a viscous incompressible fluid in a junction of unbounded channels with sources and sinks is modeled through the Navier-Stokes equations under inhomogeneous Dirichlet boundary conditions. In contrast to many previous…

Analysis of PDEs · Mathematics 2025-05-21 Filippo Gazzola , Mikhail V. Korobkov , Xiao Ren , Gianmarco Sperone

We prove the existence of a weak solution to the compressible Navier--Stokes system with singular pressure that explodes when density achieves its congestion level. This is a quantity whose initial value evolves according to the transport…

Analysis of PDEs · Mathematics 2022-02-09 Milan Pokornyý , Aneta Wróblewska-Kamińska , Ewelina Zatorska

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

We prove that any weak space-time $L^2$ vanishing viscosity limit of a sequence of strong solutions of Navier-Stokes equations in a bounded domain of ${\mathbb{R}}^2$ satisfies the Euler equation if the solutions' local enstrophies are…

Analysis of PDEs · Mathematics 2017-12-06 Peter Constantin , Vlad Vicol

We consider the 2D, incompressible Navier-Stokes equations near the Couette flow, $\omega^{(NS)} = 1 + \epsilon \omega$, set on the channel $\mathbb{T} \times [-1, 1]$, supplemented with Navier boundary conditions on the perturbation,…

Analysis of PDEs · Mathematics 2024-05-30 Jacob Bedrossian , Siming He , Sameer Iyer , Fei Wang

We consider the Navier--Stokes--Fourier system describing the motion of a compressible, viscous, and heat conducting fluid in a bounded domain with general non-homogeneous Dirichlet boundary conditions for the velocity and the absolute…

Analysis of PDEs · Mathematics 2021-06-11 Nilasis Chaudhuri , Eduard Feireisl

We consider the Navier-Stokes equations with Navier's slip boundary conditions in a three-dimensional curved thin domain around a given closed surface. Under suitable assumptions we show that the average in the thin direction of a strong…

Analysis of PDEs · Mathematics 2020-09-23 Tatsu-Hiko Miura

This work is concerned with 2D-Navier Stokes equations in a multiply-connected bounded domain with permeable walls. The permeability is described by a Navier type condition. Our aim is to show that the inviscid limit is a solution of the…

Analysis of PDEs · Mathematics 2024-09-27 N. V. Chemetov , F. Cipriano

We study the nonhomogeneous boundary value problem for Navier--Stokes equations of steady motion of a viscous incompressible fluid in a two--dimensional bounded multiply connected domain $\Omega=\Omega_1\setminus\bar{\Omega}_2,…

Mathematical Physics · Physics 2011-10-31 Mikhail V. Korobkov , Konstantin Pileckas , Remigio Russo