Asymptotic Behaviour of Solutions of Lubrication Problem in a Thin Domain with a Rough Boundary and Tresca Fluid-solid Interface Law
نویسندگان
چکیده
We study the asymptotic behavior of the solution of a Stokes flow in a thin domain, with a thickness of order ε, and a rough surface. The roughness is defined by a quasi-periodic function with period ε. We suppose that the flow is subject to a Tresca fluid-solid interface condition. We prove a new result on the lower-semicontinuity for the two-scale convergence, which allows us to obtain rigorously the limit problem and to establish the uniqueness of its solution.
منابع مشابه
Asymptotic Analysis of a Micropolar Fluid Flow in Thin Domain with a Free and Rough Boundary
Abstract. Motivated by lubrication problems, we consider a micropolar fluid flow in a 2D domain with a rough and free boundary. We assume that the thickness and the roughness are both of order 0 < ε << 1. We prove the existence and uniqueness of a solution of this problem for any value of ε and we establish some a priori estimates. Then we use the two-scale convergence technique to derive the l...
متن کاملA study of a Stefan problem governed with space–time fractional derivatives
This paper presents a fractional mathematical model of a one-dimensional phase-change problem (Stefan problem) with a variable latent-heat (a power function of position). This model includes space–time fractional derivatives in the Caputo sense and time-dependent surface-heat flux. An approximate solution of this model is obtained by using the optimal homotopy asymptotic method to find the solu...
متن کاملDarcy’s Flow with Prescribed Contact Angle – Well-posedness and Lubrication Approximation
We consider the spreading of a thin two-dimensional droplet on a solid substrate. We use a model for viscous fluids where the evolution is governed by Darcy’s Law. At the triple point where air and liquid meet the solid substrate, the liquid assumes a constant, non-zero contact angle (partial wetting). We show local and global well-posedness of this free boundary problem in the presence of the ...
متن کاملFundamental Solutions of Dynamic Poroelasticity and Generalized Termoelasticity
Fundamental solutions of dynamic poroelasticity and generalized thermoelasticity are derived in the Laplace transform domain. For poroelasticity, these solutions define the solid displacement field and the fluid pressure in fluid-saturated media due to a point force in the solid and an injection of fluid in the pores. In addition, approximate fundamental solutions for short times are derived by...
متن کاملElastic Wave Propagation at Imperfect Boundary of Micropolar Elastic Solid and Fluid Saturated Porous Solid Half-Space
This paper deals with the reflection and transmission of elastic waves from imperfect interface separating a micropolar elastic solid half-space and a fluid saturated porous solid half-space. Longitudinal and transverse waves impinge obliquely at the interface. Amplitude ratios of various reflected and transmitted waves are obtained and computed numerically for a specific model and results obta...
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 2006