Dear Colleagues,
it is with pleasure that we announce the *workshop*
*** Half day in Stochastic Analysis and applications ***
WHEN: Wednesday 30 October 2019, starting at 10:30 WHERE: Aula 1C150, Torre Archimede, via Trieste 61, Padova
*** SCHEDULE: *** 10.30: Therry Lyons (Oxford) 11.05: Franco Flandoli (SNS Pisa) 11.40: Francesco Caravenna (Milano Bicocca) 12.15: Franco Rampazzo (Padova)
Please find more details below and the poster in attachment.
Looking forward to your participation, Fabio Ancona, Paolo Dai Pra, Franco Rampazzo
---------------------------------------------------------------- *** Half day in Stochastic Analysis and applications *** Wed. 30 Oct. 2019, Aula 1C150 Maths Department, Padova
---------------- *** Special Guest: THERRY LYONS (Oxford) *** *** Opening the workshop at 10:30*** ----------------
*** Speaker: FRANCO FLANDOLI (SNS Pisa)*** *** Seminar at 11:05*** *** Title: Effect of transport noise on PDEs *** *** Abstract *** 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 in the case of 2D Euler equations and 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 Gubinelli, Priola, Barbato, Galeati, Luo and myself.
---------------- *** Speaker: FRANCESCO CARAVENNA (Milano Bicocca) *** *** Seminar at 11:40 *** *** Title: On the two-dimensional KPZ equation *** *** Abstract: *** We consider the Kardar-Parisi-Zhang (KPZ) equation in two space dimensions, driven by space-time white noise. This is a singular PDE which lacks a solution theory, so it is standard to consider a regularized version of the equation and then to investigate the behavior of the solution when the regularization is removed. We first show that the regularized solution undergoes a phase transition, as the noise strength is varied on a logarithmic scale. Then, in the sub-critical regime, we prove convergence (after centering and rescaling) to an explicit well-posed random PDE, the additive Stochastic Heat Equation, with a non-trivial constant on the noise. Based on joint works with Rongfeng Sun and Nikos Zygouras.
---------------- *** Speaker: FRANCO RAMPAZZO (Padova) *** *** Seminar at 12:15 *** *** Title: Limit solutions for control-affine nonlinear systems of ode's *** *** Abstract: *** The aim of this talk, which is fully devoted to deterministic input-output systems, is to present the extremely weak notion of 'limit solution', that might be (or might be not) of interest also for whom is more interested in Stochastic Analysis. For a nonlinear (deterministic) control system with a given initial condition and with a dynamics which is affine in the control variable, a 'limit solution' verifies the following properties: i) it is pointwise defined for an input which is (formally) the derivative of a Lebesgue integrable function; ii) in the commutative case (i.e. when all Lie brackets of the involved vector field vanish identically) the limit solution coincides with the solution one can obtain via a (existing) change of coordinates which makes all vector fields constant; iii) the notion of limit solution subsumes former concepts of solution valid for the generic, non-commutative case. In particular, when the control is the derivative of a bounded variation path, a quite clear relation is established between limit solutions and so-called 'graph completion' solutions.
Paolo Dai Pra Dipartimento di Informatica Università degli Studi di Verona Strada Le Grazie 15, 37134 Verona, Italy Tel. +390458027093