The inviscid limit behavior for smooth solutions of the Boussinesq system (Q369796)

Summary: 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.