The Inviscid Limit Behavior for Smooth Solutions of the Boussinesq System

Abstract

The inviscid limit problem for the smooth solutions of the Boussinesq system is studied in this paper. We prove the $H^s$ convergence result of this system as the diffusion and the viscosity coefficients vanish with the initial data belonging to $H^s$. Moreover, the $H^s$ convergence rate is given if we allow more regularity on the initial data.