Asymptotic behavior of solutions to the drift-diffusion equation with critical dissipation (Q295516)

The authors provide asymptotic expansions as \(t\to\infty\) for the solution of the Cauchy problem for the drift-diffusion equation with critical dissipation in \(\mathbb{R}^n\), which turn out to be different in the case \(n=2\) and \(n\geq 3\). The techniques rely on \(L^p-L^q\) estimates starting from the representation formula of the solution.