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H 2 Singular SPDE with rough coefficients

Auteurs : Otto, Felix (Auteur de la Conférence)
CIRM (Editeur )

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quasi-linear stochastic partial differential equations controlled rough path linear equation with rough coefficients parametric model integration step in rough path reconstruction step in rough path Safonov’s kernel-free approach to Schauder theory modelled distribution questions from the audience

Résumé : We are interested in parabolic differential equations $(\partial_t-a\partial_x^2)u=f$ with a very irregular forcing $f$ and only mildly regular coefficients $a$. This is motivated by stochastic differential equations, where $f$ is random, and quasilinear equations, where $a$ is a (nonlinear) function of $u$.
Below a certain threshold for the regularity of $f$ and $a$ (on the Hölder scale), giving even a sense to this equation requires a renormalization. In the framework of the above setting, we present recent ideas from the area of stochastic differential equations (Lyons' rough path, Gubinelli's controlled rough paths, Hairer's regularity structures) that allow to build a solution theory. We make a connection with Safonov's approach to Schauder theory.
This is based on joint work with H. Weber, J. Sauer, and S. Smith.

Codes MSC :
35B65 - Smoothness and regularity of solutions of PDE
60H15 - Stochastic partial differential equations

Ressources complémentaires :

    Informations sur la Vidéo

    Réalisateur : Hennenfent, Guillaume
    Langue : Anglais
    Date de publication : 22/05/2018
    Date de captation : 16/05/2018
    Collection : Partial Differential Equations ; Probability and Statistics
    Sous collection : Research talks
    Domaine : PDE ; Probability & Statistics
    Format : MP4 (.mp4) - HD
    Durée : 00:47:59
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : https://videos.cirm-math.fr/2018-05-16_Otto.mp4

Informations sur la rencontre

Nom de la rencontre : Stochastic partial differential equations / Equations aux dérivées partielles stochastiques
Organisateurs de la rencontre : Berglund, Nils ; Debussche, Arnaud ; Delarue, François ; Kuehn, Christian
Dates : 14/05/2018 - 18/05/2018
Année de la rencontre : 2018
URL Congrès : https://conferences.cirm-math.fr/1742.html

Citation Data

DOI : 10.24350/CIRM.V.19401803
Cite this video as: Otto, Felix (2018). Singular SPDE with rough coefficients. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19401803
URI : http://dx.doi.org/10.24350/CIRM.V.19401803

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