2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/171047We show a new Bernstein's inequality which generalizes the results of Cannone-Planchon, Danchin and Lemarié-Rieusset. As an application of this inequality, we prove the global well-posedness of the 2D quasi-geostrophic equation with the critical and super-critical dissipation for the small initial data in the critical Besov space, and local well-posedness for the large initial data.18pagesAnalysis of PDEs35Q35, 35Q30text