A rigorous derivation of the time-dependent Reynolds equation
نویسندگان
چکیده
We study the asymptotic behavior of solutions of the evolution Stokes equation in a thin three-dimensional domain bounded by two moving surfaces in the limit as the distance between the surfaces approaches zero. Using only a priori estimates and compactness it is rigorously verified that the limit velocity field and pressure are governed by the time-dependent Reynolds equation.
منابع مشابه
EFFECT OF TIME-DEPENDENT TRANSPIRATION ON AXISYMMETRIC STAGNATION-POINT FLOW AND HEATTRANSFER OF A VISCOUS FLUID ON A MOVING CIRCULAR CYLINDER
Effect of time dependent normal transpiration on the problem of unsteady viscous flow and heat transfer in the vicinity of an axisymmetric stagnation point of an infinite circular cylinder moving simultaneously with time-depended angular and axial velocities and with time-dependent wall temperature or wall heat flux are investigated. The impinging free stream is steady with a strain rate . A re...
متن کاملThe Quantum Statistical Mechanical Theory of Transport Processes
A new derivation of the quantum Boltzmann transport equation for the Fermion system from the quantum time evolution equation for the wigner distribution function is presented. The method exhibits the origin of the time - irreversibility of the Boltzmann equation. In the present work, the spin dependent and indistinguishibility of particles are also considered.
متن کاملRigorous derivation of the Gross-Pitaevskii equation.
The time-dependent Gross-Pitaevskii equation describes the dynamics of initially trapped Bose-Einstein condensates. We present a rigorous proof of this fact starting from a many-body bosonic Schrödinger equation with a short-scale repulsive interaction in the dilute limit. Our proof shows the persistence of an explicit short-scale correlation structure in the condensate.
متن کاملReduced Basis Approximation and A Posteriori Error Estimation for the Time-Dependent Viscous Burgers Equation
In this paper we present rigorous a posteriori L2 error bounds for reduced basis approximations of the unsteady viscous Burgers equation in one space dimension. The key new ingredient is accurate solution–dependent (Online) calculation of the exponential–in–time stability factor by the Successive Constraint Method. Numerical results indicate that the a posteriori error bounds are practicable fo...
متن کاملAixsymmetric Stagnation Point Flow of a Viscous Fluid on a Moving Cylinder with Time Dependent Axial Velocity
The unsteady viscous flow in the vicinity of an axisymmetric stagnation point of an infinite moving cylinder with time-dependent axial velocity is investigated. The impinging free stream is steady with a strain rate k. An exact solution of the Navier-Stokes equations is derived in this problem. A reduction of these equations is obtained by use of appropriate transformations. The general self-si...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Asymptotic Analysis
دوره 84 شماره
صفحات -
تاریخ انتشار 2013