Space-time localisation for the dynamic $\Phi^4_3$ model

Understand

We prove an a priori bound for solutions of the dynamic $\Phi^4_3$ equation.

• This bound provides a control on solutions on a compact space-time set only in terms of the realisation of the noise on an enlargement of this set, and it does not depend on any choice of space-time boundary conditions.
• We treat the large and small scale behaviour of solutions with completely different arguments.
• For small scales we use bounds akin to those presented in Hairer's theory of regularity structures.