Related papers: A note on viscous flow induced by half-line source…
Time-periodic solutions to the Navier-Stokes equations that govern the flow of a viscous liquid past a three-dimensional body moving with a time-periodic velocity are investigated. The net motion of the body over a full time-period is…
This paper is concerned with self-similar solutions of the steady Navier-Stokes system in a two-dimensional sector with the no-slip boundary condition. We give necessary and sufficient conditions in terms of the angle of the sector and the…
The quasi-neutral limit of the Navier-Stokes-Poisson system modeling a viscous plasma with vanishing viscosity coefficients in the half-space $\mathbb{R}^{3}_{+}$ is rigorously proved under a Navier-slip boundary condition for velocity and…
In this article, three-dimensional (3D) lid-driven flows in semicircular cavities are studied. The numerical solution of the Navier-Stokes equations modeling incompressible viscous fluid flow in cavities is obtained via a methodology…
In the present paper, we examine the viscous flow evolution in a square cavity. Coupled with the stream function, the initial-boundary value problem of the vorticity is numerically solved by a method of iteration. The only boundary…
We study the stationary Navier--Stokes equations in the region between two rotating concentric cylinders. We first prove that, under the small Reynolds number, if the fluid is axisymmetric and if its velocity is sufficiently small in the…
The incompressible Navier-Stokes equations in R^3 are shown to admit a unique axisymmetric solution without swirl if the initial vorticity is a circular vortex filament with arbitrarily large circulation Reynolds number. The emphasis is on…
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…
The planar problem of a viscous laminar flow around elliptical cylinders under angle of attack is considered. From the solution of the laminar boundary layer equations using the Loytsyansky local similarity method, the shear stress at the…
We study the stationary nonhomogeneous Navier--Stokes problem in a two dimensional symmetric domain with a semi-infinite outlet (for instance, either parabo-\\loidal or channel-like). Under the symmetry assumptions on the domain, boundary…
We study a simplified Ericksen-Leslie system modeling the flow of nematic liquid crystals with partially free boundary conditions. It is a coupled system between the Navier-Stokes equation for the fluid velocity with a transported heat flow…
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…
The evolution of the interface separating a conduit of light, viscous fluid rising buoyantly through a heavy, more viscous, exterior fluid at small Reynolds numbers is governed by the interplay between nonlinearity and dispersion. Previous…
A system of partial differential equations for a diffusion interface model is considered for the stationary motion of two macroscopically immiscible, viscous Newtonian fluids in a three-dimensional bounded domain. The governing equations…
We investigate the time-asymptotic stability of solutions to the one-dimensional Navier-Stokes-Fourier system in the half-space, focusing on the outflow and impermeable wall problems. When the prescribed boundary and far-field conditions…
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…
We study a coupled fluid-structure system involving boundary conditions on the pressure. The fluid is described by the incompressible Navier--Stokes equations in a 2D rectangular type domain where the upper part of the domain is described…
The Navier-Stokes motions in cylindrical domain with Navier boundary conditions are considered. First the existence of global regular two-dimensional solutions are proved. The solutions are bounded by the same constant for all time.…
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…
We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in $\R^n$ with compact and smooth boundary, subject to the kinematic and vorticity boundary conditions on the non-flat…