Related papers: Incompressible viscous fluid flows in a thin spher…
It is known that the three dimensional Navier-Stokes system for an incompressible fluid in the whole space has a one parameter family of explicit stationary solutions, which are axisymmetric and homogeneous of degree -1. We show that these…
In this paper, we study a free boundary problem for compressible spherically symmetric Navier-Stokes equations without a solid core. Under certain assumptions imposed on the initial data, we obtain the global existence and uniqueness of the…
We propose a two-dimensional flow model of a viscous fluid between two close moving surfaces. We show, using a formal asymptotic expansion of the solution, that its asymptotic behavior, when the distance between the two surfaces tends to…
We show a case of steady flow in a granular gas that, for small shear rates, is accurately described by Navier-Stokes hydrodynamics, even for high inelasticity. The (low density) granular gas is composed of identical inelastic spheres and…
We study the two-dimensional stationary Navier-Stokes equations with rotating effect in the whole space. The unique existence and the asymptotics of solutions are obtained without the smallness assumption on the rotation parameter.
In this note, we show the existence of regular solutions to the stationary version of the Navier-Stokes system for compressible fluids with a density dependent viscosity, known as the shallow water equations. For arbitrary large forcing we…
A model of fully developed turbulence of a compressible fluid is briefly reviewed. It is assumed that fluid dynamics is governed by a stochastic version of Navier-Stokes equation. We show how corresponding field theoretic-model can be…
In this work we investigate the existence of weak solutions for steady flows of generalized incompressible and homogeneous viscous fluids. The problem is modeled by the steady case of the generalized Navier-Stokes equations, where the…
We investigate the linear instability of flows that are stable according to Rayleigh's criterion for rotating fluids. Using Taylor-Couette flow as a primary test case, we develop large Reynolds number matched asymptotic expansion theories.…
The incompressible Navier-Stokes equations and static Euler equations are considered. We find that there exist infinite non-trivial regular solutions of incompressible static Euler equations with given boundary conditions. Moreover there…
The paper considers a two-dimensional flow in a channel, which consists of straight inlet and outlet branches and a circularly 90-degree curved bend. An incompressible viscous fluid flows through the elbow under the action of a constant…
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…
We study a moving boundary value problem consisting of a viscous incompressible fluid moving and interacting with a nonlinear elastic fluid shell. The fluid motion is governed by the Navier-Stokes equations, while the fluid shell is modeled…
We study the stability of two-fluid flow through a plane channel at Reynolds numbers of a hundred to a thousand in the linear and nonlinear regimes. The two fluids have the same density but different viscosities. The fluids, when miscible,…
First, the solution uniqueness and existence of a stationary anisotropic (linear) Stokes system with constant viscosity coefficients in a compressible framework on $n$-dimensional flat torus are analysed in a range of periodic Sobolev…
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 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…
Recent studies suggest that unstable, non-chaotic solutions of the Navier-Stokes equation may provide deep insights into fluid turbulence. In this article, we present a combined experimental and numerical study exploring the dynamical role…
We investigate the nonlinear instability of a smooth steady density profile solution of the threedimensional nonhomogeneous incompressible Navier-Stokes equations in the presence of a uniform gravitational field, including a Rayleigh-Taylor…
The Navier-Stokes equations describing laminar flow of an incompressible fluid will be solved. Different group of general solutions for Navier stokes equations governing Laminar incompressible fluids will be derived.