Probability seminar: The dynamic Φ43 model comes down from infinity
SM4, School of Mathematics
Hendrik Weber, University of Warwick
The dynamic Φ43 model comes down from infinity
We prove an a priori bound for the dynamic Φ43 model on the torus which is independent of the initial condition. In particular, this bound rules out the possibility of finite time blow-up of the solution. It also gives a uniform control over solutions at large times, and thus allows to construct invariant measures via the Krylov-Bogoliubov method. It thereby provides a new dynamic construction of the Euclidean Φ43 field theory on finite volume.
Our method is based on the local-in-time solution theory developed recently by Gubinelli, Imkeller, Perkowski and Catellier, Chouk. The argument relies entirely on deterministic PDE arguments (such as embeddings of Besov spaces and interpolation), which are combined to derive energy inequalities.