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H 2 Pathwise regularisation by noise in PDEs

Auteurs : Gubinelli, Massimiliano (Auteur de la Conférence)
CIRM (Editeur )

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regularisation by noise relevant models the averaging operator irregular functions regularity of the averaging operator method of characteristics non-linear Young integral distributional vectorflelds rough transport equation controlled rough paths modulated dispersive equations Questions

Résumé : We discuss some examples of the "good" effects of "very bad", "irregular" functions. In particular we will look at non-linear differential (partial or ordinary) equations perturbed by noise. By defining a suitable notion of "irregular" noise we are able to show, in a quantitative way, that the more the noise is irregular the more the properties of the equation are better. Some examples includes: ODE perturbed by additive noise, linear stochastic transport equations and non-linear modulated dispersive PDEs. It is possible to show that the sample paths of Brownian motion or fractional Brownian motion and related processes have almost surely this kind of irregularity. (joint work with R. Catellier and K. Chouk)

Codes MSC :
35Q53 - KdV-like (Korteweg-de Vries) equations
35R60 - PDEs with randomness, stochastic PDE
60H15 - Stochastic partial differential equations
35D30 - Weak solutions of PDE

    Informations sur la Vidéo

    Réalisateur : Hennenfent, Guillaume
    Langue : Anglais
    Date de publication : 28/05/15
    Date de captation : 13/05/15
    Sous collection : Research talks
    arXiv category : Analysis of PDEs ; Probability
    Domaine : PDE ; Probability & Statistics
    Format : QuickTime (.mov) Durée : 00:51:21
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : https://videos.cirm-math.fr/2015-05-13_Gubinelli.mp4

Informations sur la rencontre

Nom de la rencontre : Averaging and homogenization in deterministic and stochastic systems / Moyennisation et homogénéisation dans les systèmes déterministes et stochastiques
Organisateurs de la rencontre : Liverani, Carlangelo ; Melbourne, Ian ; Pavliotis, Grigorios ; Olla, Stefano
Dates : 11/05/15 - 15/05/15
Année de la rencontre : 2015
URL Congrès : http://conferences.cirm-math.fr/1198.html

Citation Data

DOI : 10.24350/CIRM.V.18762503
Cite this video as: Gubinelli, Massimiliano (2015). Pathwise regularisation by noise in PDEs. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18762503
URI : http://dx.doi.org/10.24350/CIRM.V.18762503