Asymptotic Behavior of Global Solutions to the Boussinesq Equation in Multidimensions

Abstract

The Cauchy problem for the Boussinesq equation in multidimensions is investigated. We prove the asymptotic behavior of the global solutions provided that the initial data are suitably small. Moreover, our global solutions can be approximated by the solutions to the corresponding linear equation as time tends to infinity when the dimension of space $n\ge \mathrm{3}$.