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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

We study the incompressible Navier-Stokes equations in the two-dimensional strip $\mathbb{R} \times [0,L]$, with periodic boundary conditions and no exterior forcing. If the initial velocity is bounded, we prove that the solution remains…

Analysis of PDEs · Mathematics 2015-06-18 Thierry Gallay , Sinisa Slijepcevic

We consider the damped and driven Navier--Stokes system with stress free boundary conditions and the damped Euler system in a bounded domain $\Omega\subset\mathbf{R}^2$. We show that the damped Euler system has a (strong) global attractor…

Analysis of PDEs · Mathematics 2018-08-01 Vladimir Chepyzhov , Alexei Ilyin , Sergey Zelik

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

We show that H\"{o}lder continuous incompressible Euler flows that satisfy the local energy inequality ("globally dissipative" solutions) exhibit nonuniqueness and contain examples that strictly dissipate kinetic energy. The collection of…

Analysis of PDEs · Mathematics 2022-02-08 Philip Isett

We study the global and local existence and uniqueness of solutions to the Navier-Stokes equations with anisotropic viscosity in a bounded cylindrical domain $Q=\Omega\times (0,1)$, where $\Omega$ is a star-shaped domain in $R^2$. In this…

Analysis of PDEs · Mathematics 2008-10-01 Marius Paicu , Geneviève Raugel

In this paper, we establish the existence of probabilistically strong, measure-valued solutions for the stochastic incompressible Navier--Stokes equations and prove their convergence, in the vanishing viscosity limit, to probabilistically…

Analysis of PDEs · Mathematics 2026-01-30 Benjamin Gess , Robert Lasarzik

We consider the vanishing viscosity problem for solutions of the Navier-Stokes equations with Navier boundary conditions in the half-space. We lower the currently known conormal regularity needed to establish that the inviscid limit holds.…

Analysis of PDEs · Mathematics 2024-04-29 Mustafa Sencer Aydın , Igor Kukavica

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 consider the Navier--Stokes equations for compressible heat-conducting ideal polytropic gases in a bounded annular domain when the viscosity and thermal conductivity coefficients are general smooth functions of temperature. A…

Analysis of PDEs · Mathematics 2020-09-24 Ling Wan , Tao Wang

In this paper, the initial-boundary value problem to the three-dimensional inhomogeneous, incompressible and heat-conducting Navier-Stokes equations with temperature-depending viscosity coefficient is considered in a bounded domain. The…

Analysis of PDEs · Mathematics 2020-10-19 Cheng Yu , Bijun Zuo

We consider Navier-Stokes equations for compressible viscous fluids in the one-dimensional case with general viscosity coefficients. We prove the existence of global weak solution when the initial momentum $\rho_0 u_0$ belongs to the set of…

Analysis of PDEs · Mathematics 2019-01-11 Boris Haspot

In this paper, we study the large time asymptotic behavior toward rarefaction waves for solutions to the 1-dimensional compressible Navier-Stokes equations with density-dependent viscosities for general initial data whose far fields are…

Analysis of PDEs · Mathematics 2011-09-06 Quansen Jiu , Yi Wang , Zhouping Xin

In the present paper, we study the uniform regularity and vanishing dissipation limit for the full compressible Navier-Stokes system whose viscosity and heat conductivity are allowed to vanish at different order. The problem is studied in a…

Analysis of PDEs · Mathematics 2015-08-18 Wang Yong

In this article we consider weak solutions of the three-dimensional incompressible fluid flow equations with initial data admitting a one-dimensional symmetry group. We examine both the viscous and inviscid cases. For the case of viscous…

The three-dimensional, homogeneous, incompressible Navier-Stokes equations are studied in the absence of viscosity in one direction. It is shown that there are arbitrarily large initial data generating a unique global solution, the main…

Analysis of PDEs · Mathematics 2022-02-24 Isabelle Gallagher , Alexandre Yotopoulos

We study the global existence and uniqueness of classical solutions to the three-dimensional compressible isentropic Navier-Stokes equations with vacuum and external potential forces which could be arbitrarily large provided the initial…

Analysis of PDEs · Mathematics 2011-11-10 Jing Li , Jianwen Zhang , Junning Zhao

This work is devoted to study the global behavior of viscous flows contained in a symmetric domain with complete slip boundary. In such scenario the boundary no longer provides friction and therefore the perturbation of angular velocity…

Analysis of PDEs · Mathematics 2016-12-26 Xin Liu

Consider the Cauchy problem of incompressible Navier-Stokes equations in $\mathbb{R}^3$ with uniformly locally square integrable initial data. If the square integral of the initial datum on a ball vanishes as the ball goes to infinity, the…

Analysis of PDEs · Mathematics 2019-12-18 Hyunju Kwon , Tai-Peng Tsai

In this paper, we study the asymptotic behaviors of solutions to the inhomogeneous Navier-Stokes-Vlasov system in $\mathbb{R}^{3}\times\mathbb{R}^{3}$, where the initial fluid density is allowed to vanish. We establish the uniform bound of…

Analysis of PDEs · Mathematics 2025-05-12 Hai-Liang Li , Ling-Yun Shou , Yue Zhang