A priori bounds for the dynamic fractional Φ4 model on T3 in the full subcritical regime

Esquivel, Salvador; Weber, Hendrik

Research article in digital collection | Preprint | Peer reviewed

Abstract

We show a priori bounds for the dynamic fractional Φ4 model on T3 in the full subcritical regime using the framework of Hairer's regularity structures theory. Assuming the model bounds our estimates imply global existence of solutions and existence of an invariant measure. We extend the method developed for the usual heat operator by Chandra, Moinat and Weber [CMW23] to the fractional heat operator, thereby treating a more physically relevant model. A key ingredient in this work is the development of localised multilevel Schauder estimates for the fractional heat operator which is not covered by Hairer's original work. Furthermore, the algebraic arguments from [CMW23] are streamlined significantly.

Details about the publication

Name of the repositoryarXiv e-prints
StatusPublished
Release year2024 (25/11/2024)
Language in which the publication is writtenEnglish
Link to the full texthttps://arxiv.org/abs/2411.16536
Keywordsfull subcritical regime; regularity structures; localised multilevel Schauder estimates

Authors from the University of Münster

Weber, Hendrik
Professorship of Mathematics (Prof. Weber)