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.