Regularization by noise of an averaged version of the Navier-Stokes equations
DrTheresa Lange(Bielefeld University)
Aula Mancini (Scuola Normale Superiore)
Scuola Normale Superiore
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).
[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)