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

  • Bjoern Bringmann

    Institute for Advanced Study, Princeton, USA
Invariant Gibbs measures for the three-dimensional wave equation with a Hartree nonlinearity II: Dynamics cover

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Abstract

In this two-paper series, we prove the invariance of the Gibbs measure for a threedimensional wave equation with a Hartree nonlinearity. The novelty lies in the singularity of the Gibbs measure with respect to the Gaussian free field.

In this paper, we focus on the dynamical aspects of our main result. The local theory is based on a paracontrolled approach, which combines ingredients from dispersive equations, harmonic analysis, and random matrix theory. The main contribution, however, lies in the global theory. We develop a new globalization argument, which addresses the singularity of the Gibbs measure and its consequences.

Cite this article

Bjoern Bringmann, Invariant Gibbs measures for the three-dimensional wave equation with a Hartree nonlinearity II: Dynamics. J. Eur. Math. Soc. (2023), published online first

DOI 10.4171/JEMS/1317