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Paracontrolled distributions and singular PDEs

Massimiliano Gubinelli, Peter Imkeller and Nicolas Perkowski

First issued 9 October 2012 · PDF

Abstract

We introduce an approach to study certain singular PDEs which is based on techniques from paradifferential calculus and on ideas from the theory of controlled rough paths. We illustrate its applicability on some model problems like differential equations driven by fractional Brownian motion, a fractional Burgers type SPDE driven by space-time white noise, and a non-linear version of the parabolic Anderson model with a white noise potential.

Versions

  1. Version 5 (arXiv v4) current
    15 August 2017
    arXiv comments: published version
    PDF · LaTeX source · files and digests · arXiv:1210.2684
  2. Version 4 (arXiv v3)
    24 July 2014
    arXiv comments: 54 pages. We added a global existence result for the PAM model and a proof of Hairer's reconstruction theorem via paraproducts
    PDF · LaTeX source · files and digests · arXiv:1210.2684
  3. Version 3
    written 22 July 2014, not public at the time
    PDF · TeXmacs source · files and digests
  4. Version 2 (arXiv v2)
    25 October 2013
    arXiv comments: 49 pages. New title. The paper has been completely rewritten
    PDF · LaTeX source · files and digests · arXiv:1210.2684
  5. Version 1 (arXiv v1)
    9 October 2012
    arXiv comments: 30 pages
    PDF · TeXmacs source · files and digests · arXiv:1210.2684

Cite

Massimiliano Gubinelli, Peter Imkeller and Nicolas Perkowski. Paracontrolled distributions and singular PDEs. Papers of Massimiliano Gubinelli, 2012, version 5. https://mgubi.org/papers/paper/paracontrolled-distributions/

Licence: arXiv.org perpetual, non-exclusive license to distribute; all other rights reserved to the authors

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Papers of Massimiliano Gubinelli: an OpenSheaf archive (format 0.1, a draft); this page is generated by opensheaf-py from the archive.