TY - JOUR
T1 - The Dynamic Φ34 Model Comes Down from Infinity
AU - Mourrat, Jean Christophe
AU - Weber, Hendrik
N1 - Publisher Copyright:
© 2017, The Author(s).
PY - 2017/12/1
Y1 - 2017/12/1
N2 - 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.
AB - 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.
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U2 - 10.1007/s00220-017-2997-4
DO - 10.1007/s00220-017-2997-4
M3 - Article
AN - SCOPUS:85030835247
SN - 0010-3616
VL - 356
SP - 673
EP - 753
JO - Communications In Mathematical Physics
JF - Communications In Mathematical Physics
IS - 3
ER -