Random initial conditions for semi-linear PDEs

We analyze the effect of random initial conditions on the local well--posedness of semi--linear PDEs, to investigate to what extent recent ideas on singular stochastic PDEs can prove useful in this framework

On the probabilistic Cauchy theory for nonlinear dispersive PDEs

In this note, we review some of the recent developments in the well-posedness theory of nonlinear dispersive partial differential equations with random initial data.Comment: 26 pages. To appear in Landscapes of Time-Frequency Analysis, Appl. Numer. Harmon. Ana