The Dynamic Φ34 Model Comes Down from Infinity

Jean Christophe Mourrat, Hendrik Weber

Research output: Contribution to journalArticlepeer-review


We prove an a priori bound for the dynamic Φ34 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 one to construct invariant measures via the Krylov–Bogoliubov method. It thereby provides a new dynamic construction of the Euclidean Φ34 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.

Original languageEnglish (US)
Pages (from-to)673-753
Number of pages81
JournalCommunications In Mathematical Physics
Issue number3
StatePublished - Dec 1 2017

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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