相关论文: Fundamental solutions for micropolar fluids

We explain the construction of some solutions of the Stokes system with a given set of singular points, in the sense of Caffarelli, Kohn and Nirenberg. By means of a partial regularity theorem (proved elsewhere), it turns out that we are…

Complex fluids transition from laminar to transitory flow above a critical control parameter, akin to their Newtonian counterparts. In a continuum mechanics sense, fluid elements follow the ensuing complex trajectories, giving rise to…

We introduce a general description of localised distortions in active nematics using the framework of active nematic multipoles. We give the Stokesian flows for arbitrary multipoles in terms of differentiation of a fundamental flow response…

The unsteady motion of a two-layer fluid induced by oscillatory motion of a flat plate along its length is mathematically analyzed. Two cases are considered: (i) the two-layer fluid is bounded only by the oscillating plate (Stokes' second…

The article provides an analytical solution of the Navier-Stokes equations for the case of the steady flow of an incompressible fluid between two uniformly co-rotating disks. The solution is derived from the asymptotical evolution of…

In this paper we study the equations governing the unsteady motion of an incompressible homogeneous generalized second grade fluid subject to periodic boundary conditions. We establish the existence of global-in-time strong solutions for…

Flows in porous media in the low Reynolds number regime are often modeled by the Brinkman equations. Analytical solutions to these equations are limited to standard geometries. Finite volume or element schemes can be used in more…

We investigate the existence of weak solutions to a certain system of partial differential equations, modelling the behaviour of a compressible non-Newtonian fluid for small Reynolds number. We construct the weak solutions despite the lack…

The aim of this work is to study the Navier-Stokes-Voigt equations that govern flows with non-negative density of incompressible fluids with elastic properties. For the associated non-linear initial-and boundary-value problem, we prove the…

We study the flow of a micropolar fluid in a thin domain with microstructure, i.e. a thin domain with thickness $\varepsilon$ which is perforated by periodically distributed solid cylinders of size $a_\varepsilon$. A main feature of this…

We study the second derivative effects on the constitutive relations of an uncharged parity-even Galilean fluid using the null fluid framework. Null fluids are an equivalent representation of Galilean fluids in terms of a higher dimensional…

The subject of this article is a matched microstructure model for Newtonian fluid flows in fractured porous media. This is a homogenized model which takes the form of two coupled parabolic differential equations with boundary conditions in…

In the classical one-dimensional solution of fluid dynamics equations all unknown functions depend only on time t and Cartesian coordinate x. Although fluid spreads in all directions (velocity vector has three components) the whole picture…

Two-dimensional polar liquid crystals have been discovered recently in monolayers of anisotropic molecules. Here, we provide a systematic theoretical description of liquid-crystalline phases for polar particles in two spatial dimensions.…

We develop a numerical a framework to study phoretic particle dynamics in two dimensions. The particles are modeled as chemically active rigid circles, which can emit or absorb a solute into surrounding fluid. The interaction between…

In this paper, we consider the Dirichlet problem of three-dimensional inhomogeneous incompressible micropolar equations with density-dependent viscosity. Under the assumption that the coefficients are power functions of the density, we…

We consider the Rayleigh--B\'{e}nard problem for the three--dimensional Boussinesq system for the micropolar fluid. We introduce the notion of the multivalued eventual semiflow and prove the existence of the two-space global attractor…

Periodic travelling waves at the free surface of an incompressible inviscid fluid in two dimensions under gravity are numerically computed for an arbitrary vorticity distribution. The fluid domain over one period is conformally mapped from…

T. Borrvall and J. Petersson [Topology optimization of fluids in Stokes flow, International Journal for Numerical Methods in Fluids 41 (1) (2003) 77--107] developed the first model for topology optimization of fluids in Stokes flow. They…

We consider the compressible three dimensional Navier Stokes and Euler equations. In a suitable regime of barotropic laws, we construct a set of finite energy smooth initial data for which the corresponding solutions to both equations…