2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115465Motivated by the critical dissipative quasi-geostrophic equation, we prove that drift-diffusion equations with L^2 initial data and minimal assumptions on the drift are locally Holder continuous. As an application we show that solutions of the quasi-geostrophic equation with initial L^2 data and critical diffusion (-Δ)^{1/2}, are locally smooth for any space dimension.25 pagesAnalysis of PDEstext