Energy solutions and generators of singular SPDEs
Event details
| Date | 04.04.2023 |
| Hour | 15:00 › 15:50 |
| Speaker | Nicolas Perkowski (Free University) |
| Location | |
| Category | Conferences - Seminars |
| Event Language | English |
Abstract:
Energy solutions provide probabilistic solution theories for singular SPDEs with tractable (quasi-)invariant measures, with the prototypical example being the stochastic Burgers/KPZ equation with its white noise invariant measure. Energy solutions were introduced by Gonçalves and Jara and later Gubinelli and they are based on methods from hydrodynamic limits such as replacement lemmas and martingale estimates. More recently, we used operator theory and functional analysis to construct and control infinitesimal generators in this setting, which yields (weak) well-posedness of energy solutions. Compared to pathwise approaches like regularity structures, this requires only relatively soft estimates and the method applies to some scaling (super-)critical equations. I will start with the guiding example of a diffusion in a singular divergence-free vector field, where we can understand the main ideas of energy solutions without many technicalities and we can already see some (super-)critical problems. Then I will present an abstract construction of infinitesimal generators, semigroups, and energy solutions. Finally we study applications to singular SPDEs. This is joint work with Lukas Gräfner.
Practical information
- General public
- Free