Spatial Decay for Solutions to 2-D Boussinesq System with Variable Thermal Diffusivity

In this paper, the authors derive an explicit spatial decay estimate for the time dependent flow of Boussinesq fluid with thermal conductivity depending on the temperature in a semi-infinite strip. By introducing a stream function, the authors established a decay estimate for an expression involving the stream function. To make the result explicit, an upper bound for total energy is also obtained. The results of this paper may be thought of as a version of Saint-Venant’s principle.