相关论文: On the axisymmetric Navier-Stokes flow passing a c…

Let $D$ be the exterior of a cone inside a ball, with its altitude angle at most $\pi/6$ in $\mathbb{R}^3$, which touches the $x_3$ axis at the origin. For any initial value $v_0 = v_{0,r}e_{r} + v_{0,\theta} e_{\theta} + v_{0,3} e_{3}$ in…

We investigate the global regularity problem for the three-dimensional incompressible Navier-Stokes equations restricted to axisymmetric flows in a finite cylinder $D = \{(r,\theta,x_3): 0 \le r \le 1, 0 \le \theta < 2\pi, 0 \le x_3 \le…

We prove global smooth continuation for smooth finite-energy solutions of the three-dimensional incompressible Navier--Stokes equations by a two-part first-threshold argument. Part I proves the axisymmetric-with-swirl theorem in the exact…

We consider the three-dimensional steady Navier-Stokes system in the exterior of an infinite cylinder under the action of an external force. We construct solutions in the class of vertically uniform flows which vanish at horizontal…

For the physically important case in which the viscosity coefficients depend on the density $\rho$ through a power law (i.e., $\rho^\delta$ with some exponent $\delta \in (\frac{1}{2},1)$), we establish the global well-posedness of regular…

We consider the motion of an incompressible viscous fluid on a compact Riemannian manifold $\sM$ with boundary. The motion on $\sM$ is modeled by the incompressible Navier-Stokes equations, and the fluid is subject to pure or partial slip…

Let $v$ be a solution of the axially symmetric Navier-Stokes equation. We determine the structure of certain (possible) maximal singularity of $v$ in the following sense. Let $(x_0, t_0)$ be a point where the flow speed $Q_0 = |v(x_0,…

This is the first of two papers concerning the asymptotic behavior of the incompressible Navier-Stokes equations in a half-space at high Reynolds numbers, with initial data given by a point vortex. In the present work, we establish the…

We study the stationary Navier--Stokes equations in the whole plane with a compactly supported force term and with a prescribed constant spatial limit. Prior to this work, existence of solutions to this problem was only known under special…

We construct global weak solutions of the Euler equations in an infinite cylinder $\Pi=\{x\in \mathbb{R}^{3}\ |\ x_h=(x_1,x_2),\ r=|x_h|<1\}$ for axisymmetric initial data without swirl when initial vorticity…

The full compressible Navier-Stokes system describing the motion of a viscous, compressible, heat-conductive, and Newtonian polytropic fluid is studied in a three-dimensional simply connected bounded domain with smooth boundary having a…

Smooth solutions of the stationary Navier-Stokes equations in an infinitely long pipe, equipped with the Navier-slip or Navier-Hodge-Lions boundary condition, are considered in this paper. Three main results are presented. First, when…

We consider the initial-boundary value problem (IBVP) for the isentropic compressible Navier-Stokes equations (\textbf{CNS}) in the domain exterior to a ball in $\mathbb R^d$ $(d=2\ \text{or} \ 3)$. When viscosity coefficients are given as…

The Navier-Stokes-Coriolis system is a simple model for rotating fluids, which allows to study the influence of the Coriolis force on the dynamics of three-dimensional flows. In this paper, we consider the NSC system in an infinite…

We prove existence of global regular axially-symmetric solutions to the Navier-Stokes equations in a cylindrical domain. We assume the periodic boundary conditions on the top and the bottom of the cylinder, but on the lateral part we assume…

For the Stokes system in the half space, Kang [Math.~Ann.~2005] showed that a solution generated by a compactly supported, H\"older continuous boundary flux may have unbounded normal derivatives near the boundary. In this paper we first…

Existence, uniqueness, and regularity of time-periodic solutions to the Navier-Stokes equations in the three-dimensional whole-space are investigated. We consider the Navier-Stokes equations with a non-zero drift term corresponding to the…

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…

We investigate the existence and the zero viscosity limit of steady compressible shear flow with Navier-slip boundary condition in the absence of any external force in a two-dimension domain $\Omega=(0,L)\times(0,2)$. More precisely, under…

We consider the incompressible Navier-Stokes equations in the cylinder $\R \times \T$, with no exterior forcing, and we investigate the long-time behavior of solutions arising from merely bounded initial data. Although we do not know if…