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Singular SPDE with rough coefficients
Post-edited
Authors : Otto, Felix (Author of the conference)
CIRM (Publisher )
35B65 - Smoothness and regularity of solutions of PDE
60H15 - Stochastic partial differential equations
Additional resources :
https://www.cirm-math.fr/ProgWeebly/Renc1742/Otto.pdf
CIRM (Publisher )
Abstract :
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.
MSC Codes : 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
Additional resources :
https://www.cirm-math.fr/ProgWeebly/Renc1742/Otto.pdf
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 22/05/2018 Conference Date : 16/05/2018 Subseries : Research talks arXiv category : Probability ; Mathematical Physics ; Analysis of PDEs Mathematical Area(s) : PDE ; Probability & Statistics Format : MP4 (.mp4) - HD Video Time : 00:47:59 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2018-05-16_Otto.mp4 
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Information on the Event
Event Title : Stochastic partial differential equations / Equations aux dérivées partielles stochastiquesEvent Organizers : Berglund, Nils ; Debussche, Arnaud ; Delarue, François ; Kuehn, Christian Dates : 14/05/2018 - 18/05/2018 Event Year : 2018 Event URL : https://conferences.cirm-math.fr/1742.html
Citation Data
DOI : 10.24350/CIRM.V.19401803Cite 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 |
See Also
- [Multi angle] Stochastic solutions of 2D fluids / Author of the conference Flandoli, Franco.
- [Multi angle] Asymptotics for some non-linear stochastic heat equations / Author of the conference Nualart, Eulalia.
- [Multi angle] Global solutions to elliptic and parabolic $\Phi^4$ models in Euclidean space / Author of the conference Hofmanova, Martina.
- [Multi angle] Bessel-like SPDEs / Author of the conference Zambotti, Lorenzo.
Bibliography
- 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.
