Zusammenfassung für den Vortrag am 07.01.2021 (17:00 Uhr)

Arbeitsgemeinschaft ANGEWANDTE ANALYSIS

Bjoern Bringmann (UCLA)
Invariant Gibbs measures for the three-dimensional wave equation with a Hartree nonlinearity

In this talk, we discuss the construction and invariance of the Gibbs measure for a threedimensional

wave equation with a Hartree-nonlinearity.

In the rst part of the talk, we construct the Gibbs measure and examine its properties. We discuss the

mutual singularity of the Gibbs measure and the so-called Gaussian free eld. In contrast, the Gibbs

measure for one or two-dimensional wave equations is absolutely continuous with respect to the Gaussian

free eld.

In the second part of the talk, we discuss the probabilistic well-posedness of the corresponding nonlinear

wave equation, which is needed in the proof of invariance. At the moment, this is the only theorem proving

the invariance of any singular Gibbs measure under a dispersive equation.