On Large Drift Enhancement for the Relaxation Time of Averages

Abstract: In this note we prove in a broad analytic set-up a general result characterizing the asymptotic vanishing of the $L<sup>2$-relaxation time of averages in the presence of a large incompressible drift-like term. The broad analytic set-up is analogous to that of Constantin-Kiselev-Ryzhik-Zlatos '08 or of Coti Zelati-Delgadino-Elgindi '20. A crucial role is played by the singular value gap method of Chatterjee '25, further developed by Eberle-Lörler '26.