On the optimal decay rate of global solutions to the convection-diffusion equation with zero-mass initial data

We consider the optimal decay rate of global solutions to the convection-diffusion equation with zero-mass initial data. We establish an improved decay estimate of the global solutions under the zero-mass condition. Moreover, we derive a self-similar asymptotic profile of the global solutions. This result provides necessary and sufficient conditions for attaining the improved decay rate and shows that the decay rate is optimal.