The dynamic $\Phi^4_3$ model comes down from infinity

Understand

We prove an a priori bound for the dynamic $\Phi^4_3$ model on the torus wich 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 $\Phi^4_3$ field theory on finite volume.