| Abstract: |
| We use semi--linear PDEs as a ``proof of concept`` to investigate the effect of random initial conditions for the existence of partial differential equations of evolution type. These ideas have been pioneered by Bourgain, and recently there have been a lot of activity,
since the seminal papers by Burq and Tzvetkov.
In this setting we wish to be able to answer a series of relevant questions for the subject, such as if and when a random initial condition turns out to be useful, if super--critical data are allowed, if renormalization is needed, if further ideas from the theory of singular stochastic PDEs can be borrowed, etc. |
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