Invariant Gibbs measures for the three-dimensional wave equation with a Hartree nonlinearity

  • Bjoern Bringmann (UCLA)
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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.

Katja Heid

MPI for Mathematics in the Sciences Contact via Mail

Upcoming Events of This Seminar

  • Mar 11, 2024 tba with Carlos Román Parra
  • Mar 15, 2024 tba with Esther Bou Dagher
  • May 21, 2024 tba with Immanuel Zachhuber