Invariant Gibbs measures for the three-dimensional wave equation with a Hartree nonlinearity II: Dynamics
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866916769422114816 |
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| author | Bringmann, Bjoern |
| author_facet | Bringmann, Bjoern |
| contents | In this two-paper series, we prove the invariance of the Gibbs measure for a three-dimensional 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 para-controlled 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_04616 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Invariant Gibbs measures for the three-dimensional wave equation with a Hartree nonlinearity II: Dynamics Bringmann, Bjoern Analysis of PDEs Mathematical Physics Probability 35L15, 60H30 In this two-paper series, we prove the invariance of the Gibbs measure for a three-dimensional 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 para-controlled 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. |
| title | Invariant Gibbs measures for the three-dimensional wave equation with a Hartree nonlinearity II: Dynamics |
| topic | Analysis of PDEs Mathematical Physics Probability 35L15, 60H30 |
| url | https://arxiv.org/abs/2009.04616 |