相关论文: Stationary Structures near the Kolmogorov and Pois…

We prove the existence of steady \emph{space quasi-periodic} stream functions, solutions for the Euler equation in vorticity-stream function formulation in the two dimensional channel ${\mathbb R}\times [-1,1]$. These solutions bifurcate…

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…

In this paper, we prove the uniform nonlinear structural stability of Poiseuille flows with suitably large flux for the steady Navier-Stokes system in a two-dimensional strip with arbitrary period. Furthermore, the well-posedness theory for…

In this paper, we prove the linear inviscid damping and voticity depletion phenomena for the linearized Euler equations around the Kolmogorov flow. These results confirm Bouchet and Morita's predictions based on numerical analysis. By using…

In this paper, we investigate linear stability properties of the 2D isentropic compressible Euler equations linearized around a shear flow given by a monotone profile, close to the Couette flow, with constant density, in the domain…

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…

The paper examines the issue of stability of Poiseuille type flows in regime of compressible Navier-Stokes equations in a three dimensional finite pipe-like domain. We prove the existence of stationary solutions with inhomogeneous Navier…

We study the stability of spectrally stable, strictly monotone, smooth shear flows in the 2D Navier-Stokes equations on $\mathbb{T} \times \mathbb{R}$ with small viscosity $\nu$. We establish nonlinear stability in $H^s$ for $s \geq 2$ with…

We prove nonlinear asymptotic stability of a large class of monotonic shear flows among solutions of the 2D Euler equations in the channel $\mathbb{T}\times[0,1]$. More precisely, we consider shear flows $(b(y),0)$ given by a function $b$…

In this article, we prove linear stability, scattering and inviscid damping with optimal decay rates for the linearized 2D Euler equations around a large class of strictly monotone shear flows, $(U(y),0)$, in a periodic channel under…

In this paper, we investigate the asymptotic stability threshold problem for the 2-D Navier-Stokes equations in a finite channel with no-slip boundary conditions, around monotone shear flow $(U(t,y),0)$. We establish that the flow is…

In this paper, we show the existence of real-analytic stationary Navier-Stokes flows with isotropic streamlines in all latitudes in some simply-connected flow region on a rotating round sphere. We also exclude the possibility of having a…

Kolmogorov flow in two dimensions - the two-dimensional Navier-Stokes equations with a sinusoidal body force - is considered over extended periodic domains to reveal localised spatiotemporal complexity. The flow response mimicks the forcing…

Rotation significantly influences the stability characteristics of both laminar and turbulent shear flows. This study examines the stability threshold of the three-dimensional Navier-Stokes equations with rotation, in the vicinity of the…

The 2D Euler system, which governs inviscid incompressible fluid flow, can admit infinitely many steady solutions in a given domain with slip boundary conditions. To select physical classical solutions, we investigate the vanishing…

In this paper, we investigate the incompressible steady Navier-Stokes system with Navier slip boundary condition in a two-dimensional channel. As long as the width of cross-section of the channel grows more slowly than the linear growth,…

We study small disturbances to the periodic, plane Couette flow in the 3D incompressible Navier-Stokes equations at high Reynolds number $\textbf{Re}$. We prove that for sufficiently regular initial data of size $\epsilon \leq…

We prove the existence and stability of smooth solutions to the steady Navier-Stokes equations near plane Poiseuille-Couette flow. Consequently, we also provide the zero viscosity limit of the 2D steady Navier-Stokes equations to the steady…

In this paper, we investigate the incompressible steady Navier-Stokes system with no-slip boundary condition in a two-dimensional channel. Given any flux, the existence of solutions is proved as long as the width of cross-section of the…

In this paper, we investigate the nonlinear stability of the Couette flow for the two-dimensional compressible Navier--Stokes equations at high Reynolds numbers ($Re$) regime. It was proved that if the initial data $(\rho_{in},u_{in})$…