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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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A simple construction of the dynamical $\Phi ^4_3$ model
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by Aukosh Jagannath and Nicolas Perkowski PDF
Trans. Amer. Math. Soc. 376 (2023), 1507-1522 Request permission


The $\Phi ^4_3$ equation is a singular stochastic PDE with important applications in mathematical physics. Its solution usually requires advanced mathematical theories like regularity structures or paracontrolled distributions, and even local well-posedness is highly nontrivial. Here we propose a multiplicative transformation to reduce the periodic $\Phi ^4_3$ equation to a well-posed random PDE. This leads to a simple and elementary proof of global well-posedness, which only relies on Schauder estimates, the maximum principle, and basic estimates for paraproducts, and in particular does not need regularity structures or paracontrolled distributions.
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Additional Information
  • Aukosh Jagannath
  • Affiliation: Department of Statistics and Actuarial Sciences, University of Waterloo
  • MR Author ID: 989445
  • Email:
  • Nicolas Perkowski
  • Affiliation: Institut für Mathematik, Freie Universität Berlin
  • MR Author ID: 999469
  • ORCID: 0000-0002-3078-7284
  • Email:
  • Received by editor(s): September 1, 2021
  • Published electronically: January 4, 2023
  • Additional Notes: The first author was supported by NSERC, cette recherche a été financée par CRSNG [RGPIN-2020-04597, DGECR-2020-00199]. The second author was financially supported by the DFG via Research Unit FOR2402
  • © Copyright 2023 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 376 (2023), 1507-1522
  • MSC (2020): Primary 60H17; Secondary 35S50
  • DOI:
  • MathSciNet review: 4549683