Zero Viscosity-Diffusivity Limit for the Incompressible Boussinesq Equations in Gevrey Class

Abstract

In this paper, we study the zero viscosity-diffusivity limit for the incompressible Boussinesq equations in a periodic domain in the framework of Gevrey class. We first prove that there exists an interval of time, independent of the viscosity coefficient and the diffusivity coefficient, for the solutions to the viscous incompressible Boussinesq equations. Then, based on these uniform estimates, we show that the solutions of the viscous incompressible Boussinesq equations converge to that of the ideal incompressible Boussinesq equations as the viscosity and diffusivity coefficients go to zero. Moreover, the convergence rate is also given.