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Chapitres

Singular SPDE with rough coefficients

Apparaît dans la 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.

Informations sur la vidéo

Date de captation 16/05/2018
Date de publication 22/05/2018
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.19401803
Citer cette vidéo 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

Domaine(s)

Bibliographie

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

Codes MSC

Document(s)

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

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