Asymptotic Analysis of a Micropolar Fluid Flow in Thin Domain with a Free and Rough Boundary
نویسندگان
چکیده
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 limit problem when ε tends to zero. Moreover we show that the limit velocity and micro-rotation fields are uniquely determined via auxiliary well-posed problems and the limit pressure is given as the unique solution of a Reynolds equation.
منابع مشابه
Asymptotic Analysis of a Micropolar Fluid Flow in a Thin Domain with a Free and Rough Boundary
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