Dear Colleagues, We would like to invite you to the following SPASS seminar, jointly organized by UniPi, SNS, UniFi and UniSi: *Regularization by noise of an averaged version of the Navier-Stokes equations* Theresa Lange (University of Bielefeld)

The seminar will take place on TUE, 7.11.2023 at 14:00 CET in Aula Mancini, Scuola Normale Superiore, Pisa and streamed online at the link below (*please notice the unusual venue*).

The organizers, A. Agazzi, G. Bet, A. Caraceni, F. Grotto, G. Zanco https://sites.google.com/unipi.it/spass --------------------------------------------

*Abstract: * *In [T16], the author constructs an averaged version of the deterministic three-dimensional Navier-Stokes equations (3D NSE) which experiences blow-up in finite time. In the last decades, various works have studied suitable perturbations of ill-posed deterministic PDEs in order to prevent or delay such behavior. A promising example is given by a particular choice of transport noise used in [FL21] in the context of the vorticity form of the 3D NSE, and in [FGL21] for more general models. In this talk, we analyze the model in [T16] in view of those two works and discuss the regularization skills of transport noise in the context of the averaged 3D NSE. This is joint work with Martina Hofmanová (U Bielefeld).*

*References:* *[T16] T. Tao, Finite time blowup of an averaged three-dimensional Navier-Stokes equation. Journal of the American Mathematical Society 29(3), pp. 601-674 (2016)* *[FL21] F. Flandoli, D. Luo, High mode transport noise improves vorticity blow-up control in 3D Navier-Stokes equations. Probability Theory and Related Fields 180, pp. 309-363 (2021)* *[FGL21] F. Flandoli, L. Galeati, D. Luo, Delayed blow-up by transport noise. Communications in Partial Differential Equations 46(9), pp. 1757-1788 (2021)*