Repository logo

Infoscience

  • English
  • French
Log In
Logo EPFL, École polytechnique fédérale de Lausanne

Infoscience

  • English
  • French
Log In
  1. Home
  2. Academic and Research Output
  3. Journal articles
  4. Periodic space-time homogenisation of the φ<sub>2</sub><SUP>4</SUP> equation
 
research article

Periodic space-time homogenisation of the φ24 equation

Hairer, Martin  
•
Singh, Harprit
March 1, 2025
Journal of Functional Analysis

We consider the homogenisation problem for the φ42 equation on the torus T2, namely the behaviour as ε →0 of the solutions to the equation suggestivelywritten as ∂tuε − ∇ · A(x/ε, t/ε2)∇uε = −u3ε + ξ where ξ denotes space-time white noise and A :T2×R is uniformly elliptic, periodic and Hölder continuous. When the noise is regularised at scale δ << 1 we show that any joint limit ε, δ→0 recovers the classical dynamical φ42 model. In certain regimes or if the regularisation is chosen in a specific way adapted to the problem, we show that the counterterms can be chosen as explicit local functions of A.

  • Details
  • Metrics
Type
research article
DOI
10.1016/j.jfa.2024.110762
Web of Science ID

WOS:001375441500001

Author(s)
Hairer, Martin  

EPFL

Singh, Harprit

University of Edinburgh

Date Issued

2025-03-01

Publisher

ACADEMIC PRESS INC ELSEVIER SCIENCE

Published in
Journal of Functional Analysis
Volume

288

Issue

5

Article Number

110762

Subjects

Singular SPDEs

•

Periodic homogenisation

•

Science & Technology

•

Physical Sciences

Editorial or Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
PROPDE  
FunderFunding(s)Grant NumberGrant URL

UK Research and Innovation

EP/X015688/1

Royal Society

RP\R1\191065

Available on Infoscience
December 24, 2024
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/242458
Logo EPFL, École polytechnique fédérale de Lausanne
  • Contact
  • infoscience@epfl.ch

  • Follow us on Facebook
  • Follow us on Instagram
  • Follow us on LinkedIn
  • Follow us on X
  • Follow us on Youtube
AccessibilityLegal noticePrivacy policyCookie settingsEnd User AgreementGet helpFeedback

Infoscience is a service managed and provided by the Library and IT Services of EPFL. © EPFL, tous droits réservés