STUDIES IN CONVERGENCE OF STOCHASTIC MODELS IN ROUGH-SURFACE HYDRODYNAMIC LUBRICATION THEORY

Abstract The stochastic Reynolds equation for hydrodynamic lubrication with random homogeneous roughness of the lubricated surface is studied using series expansions. In the case in which the roughness function δ ϵ C 0 ( \ gW) , we show convergence of the series for pressure and its expectation in the Sobolev space H 1 (Ω) , whereas in the case in which δ ϵ C 1 ( \ gW) , the series converge in C 2 (Ω) provided ▽δ is uniformly bounded.