For any prescribed smooth kinetic energy and special zero-mean vertical initial temperature, there exist Hoelder beta<1/3 weak solutions of the 3D Boussinesq system with thermal diffusion, with the temperature satisfying its exact energy balance.
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H\"{o}lder continuous weak solutions of the 3D Boussinesq equation with thermal diffusion
For any prescribed smooth kinetic energy and special zero-mean vertical initial temperature, there exist Hoelder beta<1/3 weak solutions of the 3D Boussinesq system with thermal diffusion, with the temperature satisfying its exact energy balance.