Institute of Mathematics

Talk

Modul:   MAT971  Stochastische Prozesse

Effect of transport noise on PDEs

Prof. Dr. Franco Flandoli talk

Date: 04.12.19  Time: 17.15 - 18.15  Room: ETH HG G 43

Linear PDEs of transport type are regularized by the addition of an extra transport term of stochastic type; this is a phenomenon discovered around 2010 and consolidated by different techniques and on different examples. However, the effect on nonlinear PDEs is much less clear. Two results for point vortex solutions and point charge solutions of 2D Euler equations and 1D Vlasov-Poisson equations respectively, indicate that a rich noise has to be considered, opposite to the linear case where a simple space-independent noise suffices to regularize. Some confirmations that such rich noise may have regularizing properties on nonlinear models came for Leray alpha model and dyadic models of turbulence.

We now have new insight into the case 3D Navier-Stokes equations, that will be explained in the talk.

The results mentioned above, the classical and the new ones, have been obtained by several authors including M. Gubinelli, E. Priola, D. Barbato, L. Galeati, D. Luo and myself.