I will discuss how to use tools from Gaussian analysis and operator semigroups together with some commutator estimates to construct Markov semigroups for some singular SPDEs. This yields in particular uniqueness for Goncalves-Jara-Gubinelli type energy solutions. The method applies to some critical equations and, in finite dimensions, even for some supercritical equations. In infinite dimensions we get Markov semigroups for supercritical equations but we lack a uniqueness result for supercritical energy solutions in infinite dimensions. The main SPDE examples where this works are of Burgers type: quadratic, divergence-free nonlinearity and Gaussian quasi-invariant measure.
This is joint work with Lukas Gräfner.
This video was produced by the University of Münster, as part of the workshop Stochastic Analysis meets QFT – critical theory.
