English
Singular SPDE with rough coefficients
Post-edited
Auteurs : Otto, Felix (Auteur de la Conférence)
CIRM (Editeur )
35B65 - Smoothness and regularity of solutions of PDE
60H15 - Stochastic partial differential equations
Ressources complémentaires :
https://www.cirm-math.fr/ProgWeebly/Renc1742/Otto.pdf
CIRM (Editeur )
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 : 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.
35B65 - Smoothness and regularity of solutions of PDE
60H15 - Stochastic partial differential equations
Ressources complémentaires :
https://www.cirm-math.fr/ProgWeebly/Renc1742/Otto.pdf
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 22/05/2018 Date de captation : 16/05/2018 Sous collection : Research talks arXiv category : Probability ; Mathematical Physics ; Analysis of PDEs Domaine : PDE ; Probability & Statistics Format : MP4 (.mp4) - HD Durée : 00:47:59 Audience : Researchers Download : https://videos.cirm-math.fr/2018-05-16_Otto.mp4 
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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, Christian Dates : 14/05/2018 - 18/05/2018 Année de la rencontre : 2018 URL Congrès : https://conferences.cirm-math.fr/1742.html
Données de citation
DOI : 10.24350/CIRM.V.19401803Citer cette vidéo: 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 |
Voir aussi
- [Multi angle] Stochastic solutions of 2D fluids / Auteur de la Conférence Flandoli, Franco.
- [Multi angle] Asymptotics for some non-linear stochastic heat equations / Auteur de la Conférence Nualart, Eulalia.
- [Multi angle] Global solutions to elliptic and parabolic $\Phi^4$ models in Euclidean space / Auteur de la Conférence Hofmanova, Martina.
- [Multi angle] Bessel-like SPDEs / Auteur de la Conférence Zambotti, Lorenzo.
Bibliographie
- Otto, F., Sauer, J., Smith, S., & Weber, H. (2018). Parabolic equations with rough coefficients and singular forcing.
- Otto, F., & Weber, H. (2016). Quasilinear SPDEs via rough paths.
