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PreprintCC BY 4.0HAL

On the parabolic Φ34 model for the harmonic oscillator II: global existence and invariant measures

  • Aurélien Deya
  • Reika Fukuizumi
  • Laurent Thomann
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Abstract

We establish an a priori bound for the dynamical parabolic Φ34 model with harmonic potential. This bound yields the global well-posedness of the equation and, via the Krylov-Bogoliubov method, the existence of an invariant measure, shown to be non-Gaussian. The argument builds on the strategy developed by Mourrat and Weber for the periodic Φ34 model, with substantial modifications to handle the non-compact geometry of ℝ3 and the spectral framework imposed by the harmonic oscillator. We further prove that this measure is unique in the small-coupling regime.

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Cite

BibTeXRIS
BibTeX
@misc{deya2026parabolic,
  title = {{On the parabolic $\Phi_3^4$ model for the harmonic oscillator II: global existence and invariant measures}},
  author = {Aurélien Deya and Reika Fukuizumi and Laurent Thomann},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  url = {https://hal.science/hal-05733963v1},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On the parabolic Φ_3^4 model for the harmonic oscillator II: global existence and invariant measures
AU  - Aurélien Deya
AU  - Reika Fukuizumi
AU  - Laurent Thomann
PY  - 2026
DA  - 2026/09/01
PB  - HAL
UR  - https://hal.science/hal-05733963v1
AB  - We establish an a priori bound for the dynamical parabolic Φ_3^4 model with harmonic potential. This bound yields the global well-posedness of the equation and, via the Krylov-Bogoliubov method, the existence of an invariant measure, shown to be non-Gaussian. The argument builds on the strategy developed by Mourrat and Weber for the periodic Φ_3^4 model, with substantial modifications to handle the non-compact geometry of ℝ^3 and the spectral framework imposed by the harmonic oscillator. We further prove that this measure is unique in the small-coupling regime.
ER  -