Nečas Center for Mathematical Modeling Asymptotic properties of solutions to the equations of incompressible fluid mechanics
نویسنده
چکیده
Well-accepted hypothesis in the fluid dynamics is that if the boundary of the physical domain is impermeable then the viscous fluid adheres completely to it. Many authors recently proposed mathematical justifications for this hypothesis using the so-called rugous boundary. In this Paper we want to discuss optimality of results obtained in Bucur et al. [3], Bucur and Feireisl [4] or Dı́az et al. [5] and we show several corresponding examples. Finally, we extend these results for more general domains.
منابع مشابه
Concerning the Effect of a Viscoelastic Foundation on the Dynamic Stability of a Pipeline System Conveying an Incompressible Fluid
In this paper, we present an analytical method for solving a well-posed boundary value problem of mathematical physics governing the vibration characteristics of an internal flow propelled fluid-structure interaction where the pipeline segment is idealized as an elastic hollow beam conveying an incompressible fluid on a viscoelastic foundation. The effect of Coriolis and damping forces on the o...
متن کاملNonlinear analytical solution of nearly incompressible hyperelastic cylinder with variable thickness under non-uniform pressure by perturbation technique
In this paper, nonlinear analytical solution of pressurized thick cylindrical shells with variable thickness made of hyperelastic materials is presented. The governing equilibrium equations for the cylindrical shell with variable thickness under non-uniform internal pressure are derived based on first-order shear deformation theory (FSDT). The shell is assumed to be made of isotropic and homoge...
متن کاملThe Inviscid Limit and Boundary Layers for Navier-Stokes flows
The validity of the vanishing viscosity limit, that is, whether solutions of the Navier-Stokes equations modeling viscous incompressible flows converge to solutions of the Euler equations modeling inviscid incompressible flows as viscosity approaches zero, is one of the most fundamental issues in mathematical fluid mechanics. The problem is classified into two categories: the case when the phys...
متن کاملThermo-mechanical nonlinear vibration analysis of fluid-conveying structures subjected to different boundary conditions using Galerkin-Newton-Harmonic balancing method
The development of mathematical models for describing the dynamic behaviours of fluid conveying pipes, micro-pipes and nanotubes under the influence of some thermo-mechanical parameters results into nonlinear equations that are very difficult to solve analytically. In cases where the exact analytical solutions are presented either in implicit or explicit forms, high skills and rigorous mathemat...
متن کاملNečas Center for Mathematical Modeling On Pressure Boundary Conditions for Steady Flows of Incompressible Fluids with Pressure and Shear Rate Dependent Viscosities
We consider a class of incompressible fluids whose viscosities depend on the pressure and the shear rate. Suitable boundary conditions on the surface force at the inflow/outflow part of boundary are given. As an advantage of this, the mean value of the pressure over the domain is no more a free parameter which would have to be prescribed otherwise. We prove the existence and the uniqueness of w...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008