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
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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)