Description
An SPDE model: the $\Phi_3^4$ equation for the harmonic oscillator
We will first present the physical motivations behind this model, then turn to the comparison with its "standard" counterpart, in which the harmonic oscillator (on $\mathbb{R}^3$) is replaced by the Laplacian on the torus.
The results, from joint work with Reika Fukuizumi (Tokyo) and Laurent Thomann (Nancy), include the interpretation of the model in the renormalized sense, the global existence and uniqueness of a solution, the existence of an invariant measure, and finally its uniqueness in the weak nonlinearity regime.