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H 2 Singular SPDE with rough coefficients

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

 Loading the player... 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 :
https://www.cirm-math.fr/ProgWeebly/Renc1742/Otto.pdf

 Informations sur la Vidéo Langue : Anglais Date de publication : 22/05/2018 Date de captation : 16/05/2018 Collection : Research talks ; Partial Differential Equations ; Probability and Statistics Format : MP4 (.mp4) - HD Durée : 00:47:59 Domaine : PDE ; Probability & Statistics 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 stochastiquesOrganisateurs de la rencontre : Berglund, Nils ; Debussche, Arnaud ; Delarue, François ; Kuehn, ChristianDates : 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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