相关论文: Fundamental solutions for micropolar fluids

We present four different ways of deriving the Oseen tensor which is the fundamental solution to the Stokes equations for an incompressible viscous fluid. This solution corresponds to a point force acting on an infinite fluid. The…

For many biological systems that involve elastic structures immersed in fluid, small length scales mean that inertial effects are also small, and the fluid obeys the Stokes equations. One way to solve the model equations representing such…

The aim of these notes is to present in a comprehensive and relatively self-contained way some recent developments in the mathematical analysis of two-dimensional viscous flows. We consider the incompressible Navier-Stokes equations in the…

We consider the flow of a Newtonian fluid in a three-dimensional domain, rotating about a vertical axis and driven by a vertically invariant horizontal body-force. This system admits vertically invariant solutions that satisfy the 2D…

Motivated by lubrication problems, we consider a micropolar uid ow in a 2D domain with a rough and free boundary. We assume that the thickness and the roughness are both of order 0 < " << 1. We prove the existence and uniqueness of a…

We consider a multiphysics model for the flow of Newtonian fluid coupled with Biot consolidation equations through an interface, and incorporating total pressure as an unknown in the poroelastic region. A new mixed-primal finite element…

This investigation deals with some exact solutions of the equations governing the steady plane motions of an incompressible third grade fluid by using complex variables and complex functions. Some of the solutions admit, as particular…

In this paper, we study the existence of weak solutions to a steady system that describes the motion of a micropolar electrorheological fluid. The constitutive relations for the stress tensors belong to the class of generalized Newtonian…

In the present work we formulated the boundary-value-problem, comprising partial differential equations (PDEs) of steady flow for laminar/turbulent circular jet of a micropolar fluid. A new boundary layer-similarity transformation/solution…

We study a diffuse interface model describing the complex rheology and the interfacial dynamics during phase separation in a polar liquid-crystalline emulsion. More precisely, the physical systems comprises a two-phase mixture consisting in…

Stokes flow equations, used to model creeping flow, are a commonly used simplification of the Navier--Stokes equations. The simplification is valid for flows where the inertial forces are negligible compared to the viscous forces. In…

In this paper we present a mathematical analysis for a steady-state laminar boundary layer flow, governed by the Ostwald-de Wael power-law model of an incompressible non- Newtonian fluid past a semi-infinite power-law stretched flat plate…

Electron transport in two-dimensional conducting materials such as graphene, with dominant electron-electron interaction, exhibits unusual vortex flow that leads to a nonlocal current-field relation (negative resistance), distinct from the…

The existence and uniqueness of the local strong solution to the three-dimensional compressible viscoelastic fluids near the equilibrium is established. In addition to the uniform estimates on the velocity, some essential uniform estimates…

In this paper, we investigate fractional energy methods for Micropolar fluids, starting with an initial angular velocity of negative Sobolev regularity. For the initial angular velocity assumption, we consider a non-homogeneous Sobolev norm…

We examine the long-time behavior of solutions (and their derivatives) to the micropolar equations with nonlinear velocity damping. Additionally, we get a speed-up gain of $ t^{1/2} $ for the angular velocity, consistent with established…

We computationally study the flow of Newtonian fluids through sinusoidal expansion-contraction microchannels at low Reynolds number. We first use a perturbation method to analytically derive series solutions for the stream function and…

We present a number of exact solutions to the linearised Grad equations for non-equilibrium rarefied gas flows and heat flows. The solutions include the flow and pressure fields associated to a point force placed in a rarefied gas flow…

We study the two-phase Stokes flow driven by surface tension for two fluids of different viscosities, separated by an asymptotically flat interface representable as graph of a differentiable function. The flow is assumed to be…

In this paper, we consider the three dimensional Cauchy problem of the compressible micropolar viscous flows, we prove the existence of unique global classical solution for smooth initial data with small initial energy but possibly large…