Zero Viscosity-Diffusivity Limit for the Incompressible Boussinesq Equations in Gevrey Class (Communications in Mathematical Research, 2022)
In this paper, we study the zero viscosity-diffusivity limit for theincompressible Boussinesq equations in a periodic domain in the framework ofGevrey class. We first prove that there exists an interval of time, independent ofthe viscosity coefficient and the diffusivity coefficient, for the solutions to theviscous incompressible Boussinesq equations. Then, based on these uniformestimates, we show that the solutions of the viscous incompressible Boussinesqequations converge to that of the ideal incompressible Boussinesq equations asthe viscosity and diffusivity coefficients go to zero. Moreover, the convergencerate is also given.