Second Order Commutator Estimates in Renormalisation Theory for SPDEs with Gradient-Type Noise

Research output: Chapter in Book/Conference proceedingBook Chapterpeer-review

Abstract

An important step in standard renormalisation arguments involves convolution against a standard mollifier. As pointed out in (Punshon-Smith–Smith 2018), this generates second order commutator terms in equations with gradient-type noise. These are commutators similar to commutators in the well-known “folklore lemma” of Di Perna–Lions (Di Perna–Lions 1989, Lemma II.1), but not covered by standard renormalisation theory. In this note we establish the vanishing of these commutators for gradient-type noises on Td not necessarily possessing divergence-free structure.

Original languageEnglish
Title of host publicationSEMA SIMAI Springer Series
PublisherSpringer Science and Business Media Deutschland GmbH
Pages331-340
Number of pages10
DOIs
Publication statusPublished - 2024
Externally publishedYes

Publication series

NameSEMA SIMAI Springer Series
Volume34
ISSN (Print)2199-3041
ISSN (Electronic)2199-305X

Keywords

  • Commutator estimates
  • Gradient type noise
  • Renormalisation
  • Weak solutions

ASJC Scopus subject areas

  • Computational Mechanics
  • Numerical Analysis
  • Agricultural and Biological Sciences (miscellaneous)
  • Physics and Astronomy (miscellaneous)
  • Fluid Flow and Transfer Processes
  • Computational Mathematics
  • Industrial and Manufacturing Engineering
  • Applied Mathematics

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