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- W3084031666 abstract "In this two-paper series, we prove the invariance of the Gibbs measure for a three-dimensional wave equation with a Hartree nonlinearity. The main novelty is the singularity of the Gibbs measure with respect to the Gaussian free field. The singularity has several consequences in both measure-theoretic and dynamical aspects of our argument. In this paper, we construct and study the Gibbs measure. Our approach is based on earlier work of Barashkov and Gubinelli for the $Phi^4_3$-model. Most importantly, our truncated Gibbs measures are tailored towards the dynamical aspects in the second part of the series. In addition, we develop new tools dealing with the non-locality of the Hartree interaction. We also determine the exact threshold between singularity and absolute continuity of the Gibbs measure depending on the regularity of the interaction potential." @default.
- W3084031666 created "2020-09-14" @default.
- W3084031666 creator A5033988397 @default.
- W3084031666 date "2020-09-10" @default.
- W3084031666 modified "2023-09-27" @default.
- W3084031666 title "Invariant Gibbs measures for the three-dimensional wave equation with a Hartree nonlinearity I: Measures" @default.
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