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This paper is concerned with the study of nonlinear stability of superposition of boundary layer and rarefaction wave on the two-fluid Navier-Stokes-Poisson system in the half line $\mathbb{R}_{+}=:(0,+\infty)$. On account of the…

Analysis of PDEs · Mathematics 2015-08-07 Haiyan Yin , Jinshun Zhang , Changjiang Zhu

In this paper, we study the Vlasov-Navier-Stokes system in a 2D pipe with partially absorbing boundary conditions. We show the existence of stationary states for this system near small Poiseuille flows for the fluid phase, for which the…

Analysis of PDEs · Mathematics 2016-12-21 Olivier Glass , Daniel Han-Kwan , Ayman Moussa

The Navier-Stokes equations in a two-dimensional exterior domain are considered. The asymptotic stability of stationary solutions satisfying a general hypothesis is proven under any $L^2$-perturbation. In particular the general hypothesis…

Analysis of PDEs · Mathematics 2017-03-21 Julien Guillod

This paper studies the two-dimensional inhomogeneous Navier--Stokes equations governing stratified flows in a bounded domain under a gravitational potential \(f\). Our main results are as follows. First, we provide a rigorous…

Analysis of PDEs · Mathematics 2025-12-23 Song Jiang , Quan Wang

This paper is concerned with the large time behavior of the Cauchy problem for Navier-Stokes/Allen-Cahn system describing the interface motion of immiscible two-phase flow in 3-D. The existence and uniqueness of global solutions and the…

Analysis of PDEs · Mathematics 2021-10-28 Yazhou Chen , Hakho Hong , Xiaoding Shi

When an upstream steady uniform supersonic flow impinges onto a symmetric straight-sided wedge, governed by the Euler equations, there are two possible steady oblique shock configurations if the wedge angle is less than the detachment angle…

Analysis of PDEs · Mathematics 2019-01-18 Gui-Qiang G. Chen

The stability of idealized shear flow at long wavelengths is studied in detail. A hydrodynamic analysis at the level of the Navier-Stokes equation for small shear rates is given to identify the origin and universality of an instability at…

Condensed Matter · Physics 2009-10-30 Jose M. Montanero , Andres Santos , Mirim Lee , James W. Dufty , J. F. Lutsko

We consider the vorticity form of the Navier-Stokes equations on the two-dimensional unit sphere and study the nonlinear stability of the two-jet Kolmogorov type flow which is a stationary solution given by the zonal spherical harmonic…

Analysis of PDEs · Mathematics 2023-02-22 Tatsu-Hiko Miura

We investigate the global in time stability of regular solutions with large velocity vectors to the evolutionary Navier-Stokes equation in ${\bf R}^3$. The class of stable flows contains all two dimensional weak solutions. The only…

Analysis of PDEs · Mathematics 2007-05-23 Piotr B. Mucha

We treat the 1D shock tube problem, establishing existence of steady solutions of full (nonisentropic) polytropic gas dynamics with arbitrary noncharacteristic data. We present also numerical experiments indicating uniqueness and…

Analysis of PDEs · Mathematics 2023-04-13 Blake Barker , Benjamin Melinand , Kevin Zumbrun

We consider the Nernst-Planck-Stokes system on a bounded domain of $\mathbb{R}^d$, $d=2,3$ with general nonequilibrium Dirichlet boundary conditions for the ionic concentrations. It is well known that, in a wide range of cases, equilibrium…

Analysis of PDEs · Mathematics 2025-01-09 Fizay-Noah Lee

In cylindrical domain, we consider the nonstationary flow with prescribed inflow and outflow, modelled with Navier-Stokes equations under the slip boundary conditions. Using smallness of some derivatives of inflow function, external force…

Analysis of PDEs · Mathematics 2015-05-27 Joanna Renclawowicz , Wojciech M. Zajaczkowski

We present the existence/non-existence criteria for large-amplitude boundary layer solutions to the inflow problem of the one-dimensional (1D) full compressible Navier-Stokes equations on a half line $\mathbb{R}_+$. Instead of the classical…

Analysis of PDEs · Mathematics 2025-05-01 Yi Wang , Yong-Fu Yang , Qiuyang Yu

In this work the existence of weak solutions for a class of non-Newtonian viscous fluid problems is analyzed. The problem is modeled by the steady case of the generalized Navier-Stokes equations, where the exponent $q$ that characterizes…

Analysis of PDEs · Mathematics 2012-04-02 Hermenegildo Borges de Oliveira

We prove a stability threshold theorem for 2D Navier-Stokes on three unbounded domains: the whole plane $\mathbb{R} \times \mathbb{R}$, the half plane $\mathbb{R} \times [0,\infty)$ with Navier boundary conditions, and the infinite channel…

Analysis of PDEs · Mathematics 2025-03-11 Ryan Arbon , Jacob Bedrossian

We show that a steady-state solution ${\bf U}$ to the system of equations of a Navier-Stokes flow past a rotating body is nonlinearly unstable if the associated linear operator $\cal L$ has a part of the spectrum in the half-plane…

Analysis of PDEs · Mathematics 2020-01-28 Giovanni P. Galdi Jiří Neustupa

Dufty, Lee, Lutsko, Montanero, and Santos have carried out stability analyses of steady stationary shear flows. Their approach is based on the compressible and heat conducting Navier-Stokes-Fourier model. It predicts the unstable…

Statistical Mechanics · Physics 2012-03-27 Wm. G. Hoover , Carol G. Hoover

In this study we revisit the problem of computing steady Navier-Stokes flows in two-dimensional unbounded domains. Precise quantitative characterization of such flows in the high-Reynolds number limit remains an open problem of theoretical…

Fluid Dynamics · Physics 2015-01-26 Jonathan Gustafsson , Bartosz Protas

Large-time behavior of solutions to the inflow problem of full compressible Navier-Stokes equations is investigated on the half line $R^+ =(0,+\infty)$. The wave structure which contains four waves: the transonic(or degenerate) boundary…

Analysis of PDEs · Mathematics 2015-05-19 Xiaohong Qin , Yi Wang

Due to computational complexity, fluid flow problems are mostly defined on a bounded domain. Hence, capturing fluid outflow calls for imposing an appropriate condition on the boundary where the said outflow is prescribed. Usually, the…

Analysis of PDEs · Mathematics 2021-09-22 John Sebastian H. Simon , Hirofumi Notsu