Related papers: Prandtl-Batchelor flows on an annulus
In this paper, we establish vanishing viscosity limit of the 2D Navier-Stokes equations in a horizontally periodic strip. On the vertical direction, the horizontal component of the velocity is subjected to two different types of boundary…
We investigate the Couette-Taylor problem for a steady incompressible viscous fluid in a 3D cylindrical annulus, where one of the two cylinders is still, under both Dirichlet and boundary conditions involving the vorticity that naturally…
We are concerned with rigidity properties of steady Euler flows in two-dimensional bounded annuli. We prove that in an annulus, a steady flow with no interior stagnation point and tangential boundary conditions is a circular flow, which…
We consider rigidity properties of steady Euler flows in two-dimensional bounded domains. We prove that steady Euler flows in a disk with exactly one interior stagnation point and tangential boundary conditions must be circular flows, which…
Numerical solutions of the laminar Prandtl boundary-layer and Navier-Stokes equations are considered for the case of the two-dimensional uniform flow past an impulsively-started circular cylinder. We show how Prandtl's solution develops a…
We study the boundary layer theory for slightly viscous stationary flows forced by an imposed slip velocity at the boundary. According to the theory of Prandtl (1904) and Batchelor (1956), any Euler solution arising in this limit and…
A semi-explicit formula of solution to the boundary layer system for thermal layer derived from the compressible Navier-Stokes equations with the non-slip boundary condition when the viscosity coefficients vanish is given, in particular in…
We study the immersed boundary problem in 2-D. It models a 1-D elastic closed string immersed and moving in a fluid that fills the entire plane, where the fluid motion is governed by the 2-D incompressible Navier-Stokes equation with a…
We study the high Reynolds number limit of a viscous fluid in the presence of a rough boundary. We consider the two-dimensional incompressible Navier-Stokes equations with Navier slip boundary condition, in a domain whose boundaries exhibit…
In this paper, we consider the zero-viscosity limit of the 2D steady Navier-Stokes equations in $(0,L)\times\mathbb{R}^+$ with non-slip boundary conditions. By estimating the stream-function of the remainder, we justify the validity of the…
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,…
In this article we consider viscous flow in the exterior of an obstacle satisfying the standard no-slip boundary condition at the surface of the obstacle. We seek conditions under which solutions of the Navier-Stokes system in the exterior…
Despite the physical importance, there are limited mathematical theories for the compressible Navier-Stokes equations with strong boundary layers. This is mainly due to the absence of a stream function structure, unlike the extensively…
We consider incompressible flows between two transversely vibrating solid walls and construct an asymptotic expansion of solutions of the Navier-Stokes equations in the limit when both the amplitude of vibrations and the thickness of the…
The present paper is concerned with an inviscid limit problem of radially symmetric stationary solutions for an exterior problem in $\mathbb{R}^n (n\ge 2)$ to compressible Navier-Stokes equation, describing the motion of viscous barotropic…
The problems of numerical modeling of viscous incompressible fluid flows are widely considered in computational fluid dynamics. Stationary solutions of boundary value problems for the Navier-Stokes equations exist at large Reynolds numbers,…
The steady motion of a viscous incompressible fluid in distorted pipes, of finite length, is modeled through the Navier-Stokes equations with mixed boundary conditions: the inflow is given by an arbitrary member of the Lions-Magenes class…
In this paper we investigate the uniqueness of solutions of the steady planar Navier-Stokes equations with different boundary conditions in the exterior domain. For a class of incompressible flow with constant vorticity, we prove the…
In this paper, we show that the spatio-temporal evolution of incompressible flows in a long circular pipe can be described by vorticity dynamics. The principal techniques to obtain solutions are similar to those used for flows in the whole…
Numerical calculations of the 2-D steady incompressible driven cavity flow are presented. The Navier-Stokes equations in streamfunction and vorticity formulation are solved numerically using a fine uniform grid mesh of 601x601. The steady…