On the parabolic $Φ_3^4$ model for the harmonic oscillator II: global existence and invariant measures
Year: 2026
Type: preprint
Abstract: 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 $\mathbb{R}^3$ and the spectral framework imposed by the harmonic oscillator. We further prove that this measure is unique in the small-coupling regime.
Source: arXiv (Cornell University)
Institution: Institut Élie Cartan de Lorraine
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212412943