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This paper is a continuation of our previous work (arXiv:2507.03505), where the global existence and incompressible limit of weak solutions to the isentropic compressible Navier-Stokes equations in the half-plane with ripped density and…

Analysis of PDEs · Mathematics 2025-10-28 Shuai Wang , Guochun Wu , Xin Zhong

In this work, we investigate the small-time global exact controllability of the Navier-Stokes equation, both towards the null equilibrium state and towards weak trajectories. We consider a viscous incompressible fluid evolving within a…

Analysis of PDEs · Mathematics 2017-03-07 Jean-Michel Coron , Frédéric Marbach , Franck Sueur

The question what information is necessary for determination of a unique solution of hydrodynamic equations for ideal fluid is investigated. Arbitrary inviscid flows of the barotropic fluid and of incompressible fluid are considered. After…

General Physics · Physics 2007-05-23 Yuri A. Rylov

We propose a two-dimensional flow model of a viscous fluid between two close moving surfaces. We show that its asymptotic behavior, when the distance between the two surfaces tends to zero, is the same as that of the the Navier-Stokes…

Analysis of PDEs · Mathematics 2022-06-09 José M. Rodríguez , Raquel Taboada-Vázquez

We consider the evolutionary MHD systems, and study the the regularity and vanishing viscosity limit of the 3-D viscous system in a class of bounded domains with a slip boundary condition. We derive the convergence is in H^{2k+1}, for k>0,…

Analysis of PDEs · Mathematics 2010-09-08 Xiaoqiang Xie , Changmin Li

We consider the zero viscosity limit of the incompressible Navier-Stokes equations with non-slip boundary condition in the half-space for the initial vorticity located away from the boundary. By using the vorticity formulation and…

Analysis of PDEs · Mathematics 2016-09-14 Mingwen Fei , Tao Tao , Zhifei Zhang

We establish convergence as the viscosity vanishes of solutions of the Navier-Stokes equations to a solution of the Euler equations for inflow, outflow boundary conditions. We extend the approach of Temam and Wang 2002, allowing the…

Analysis of PDEs · Mathematics 2025-06-24 Michael A. Gulas , James P. Kelliher

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

For periodic initial data with the density allowing vacuum, we establish the global existence and exponential decay of weak, strong and classical solutions to the two-dimensional(2D) compressible Navier-Stokes equations when the bulk…

Analysis of PDEs · Mathematics 2025-07-03 Qinghao Lei , Chengfeng Xiong

For steady two-dimensional Navier-Stokes flows with a single eddy (i.e. nested closed streamlines) in a simply connected domain, Prandtl (1905) and Batchelor (1956) found that in the inviscid limit, the vorticity is constant inside the…

Analysis of PDEs · Mathematics 2023-08-11 Mingwen Fei , Chen Gao , Zhiwu Lin , Tao Tao

Many physical systems of interest involve the close interaction of a flow in a domain with complex, time-varying boundaries. Treatment of boundaries of this nature is cumbersome due to the difficulty in explicitly tracking boundaries that…

Fluid Dynamics · Physics 2025-02-25 Emma M. Boyd , Eric Sandall , Maycon Meier , J. Matt Quinlan , Brandon Runnels

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 study a system describing the compressible barotropic fluids interacting with (visco) elastic solid shell/plate. In particular, the elastic structure is part of the moving boundary of the fluid, and the Navier-slip type boundary…

Analysis of PDEs · Mathematics 2026-05-20 Yadong Liu , Sourav Mitra , Šárka Nečasová

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

The conventional boundary conditions at the interface between two flowing liquids include continuity of the tangential velocity. We have tested this assumption with molecular dynamics simulations of Couette and Poiseuille flows of…

Soft Condensed Matter · Physics 2009-11-11 Joel Koplik , Jayanth R. Banavar

We consider the flow of an { ideal} fluid in a 2D-bounded domain, admitting flows through the boundary of this domain. The flow is described by Euler equations with \textit{non-homogeneous } Navier slip boundary conditions. These conditions…

Analysis of PDEs · Mathematics 2024-09-25 N. V. Chemetov , S. N. Antontsev

In this paper, we establish the short time inviscid limit of the incompressible Navier-Stokes equations with critical Navier-slip boundary conditions for analytic data on half-space, a boundary condition that is physically derived from the…

Analysis of PDEs · Mathematics 2019-05-01 Trinh T. Nguyen

We derive the incompressible Euler equations with heat convection with the no-penetration boundary condition from the Boltzmann equation with the diffuse boundary in the hydrodynamic limit for the scale of large Reynold number. Inspired by…

Analysis of PDEs · Mathematics 2021-04-07 Yunbai Cao , Juhi Jang , Chanwoo Kim

We establish the vanishing viscosity limit of viscous Burgers-Vlasov equations for one dimensional kinetic model about interactions between a viscous fluid and dispersed particles by using compensated compactness technique and the evolution…

Analysis of PDEs · Mathematics 2020-06-09 Wentao Cao , Teng Wang

For a natural number $m \ge 2$, we study $m$ layers of finite depth, horizontally infinite, viscous, and incompressible fluid bounded below by a flat rigid bottom. Adjacent layers meet at free interface regions, and the top layer is bounded…

Analysis of PDEs · Mathematics 2020-08-18 Noah Stevenson , Ian Tice