Asymptotic expansion of solutions to the drift-diffusion equation with large initial data

We consider the large-time behavior of the solution to the initial value problem for the Nernst–Planck type drift-diffusion equation in whole spaces. In the Lp-framework, the global existence and the decay of the solution were shown. Moreover, the second-order asymptotic expansion of the solution as t→∞ was derived. We also deduce the higher-order asymptotic expansion of the solution. Especially, we discuss the contrast between the odd-dimensional case and the even-dimensional case.