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Singular SPDE with rough coefficients

Appears in collection : Stochastic partial differential equations / Equations aux dérivées partielles stochastiques

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.

Information about the video

Date of recording 16/05/2018
Date of publication 22/05/2018
Institution CIRM
Licence CC BY NC ND
Language English
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19401803
Cite this video OTTO, Felix (16/05/2018). Singular SPDE with rough coefficients. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19401803
URL https://dx.doi.org/10.24350/CIRM.V.19401803

Domain(s)

Bibliography

Otto, F., Sauer, J., Smith, S., & Weber, H. (2018). Parabolic equations with rough coefficients and singular forcing. <arXiv:1803.07884> - https://arxiv.org/abs/1803.07884
Otto, F., & Weber, H. (2016). Quasilinear SPDEs via rough paths. <arXiv:1605.09744> - https://arxiv.org/abs/1605.09744

MSC codes

Document(s)

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

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