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Pathwise regularisation by noise in PDEs
Post-edited
Authors : Gubinelli, Massimiliano (Author of the conference)
CIRM (Publisher )
35Q53 - KdV-like (Korteweg-de Vries) equations
35R60 - PDEs with randomness, stochastic PDE
60H15 - Stochastic partial differential equations
35D30 - Weak solutions of PDE
CIRM (Publisher )
Abstract :
We discuss some examples of the "good" effects of "very bad", "irregular" functions. In particular we will look at non-linear differential (partial or ordinary) equations perturbed by noise. By defining a suitable notion of "irregular" noise we are able to show, in a quantitative way, that the more the noise is irregular the more the properties of the equation are better. Some examples includes: ODE perturbed by additive noise, linear stochastic transport equations and non-linear modulated dispersive PDEs. It is possible to show that the sample paths of Brownian motion or fractional Brownian motion and related processes have almost surely this kind of irregularity. (joint work with R. Catellier and K. Chouk)
MSC Codes : 35Q53 - KdV-like (Korteweg-de Vries) equations
35R60 - PDEs with randomness, stochastic PDE
60H15 - Stochastic partial differential equations
35D30 - Weak solutions of PDE
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 28/05/15 Conference Date : 13/05/15 Subseries : Research talks arXiv category : Analysis of PDEs ; Probability Mathematical Area(s) : PDE ; Probability & Statistics Format : QuickTime (.mov) Video Time : 00:51:21 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2015-05-13_Gubinelli.mp4 
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Information on the Event
Event Title : Averaging and homogenization in deterministic and stochastic systems / Moyennisation et homogénéisation dans les systèmes déterministes et stochastiquesEvent Organizers : Liverani, Carlangelo ; Melbourne, Ian ; Pavliotis, Grigorios ; Olla, Stefano Dates : 11/05/15 - 15/05/15 Event Year : 2015 Event URL : http://conferences.cirm-math.fr/1198.html
Citation Data
DOI : 10.24350/CIRM.V.18762503Cite this video as: Gubinelli, Massimiliano (2015). Pathwise regularisation by noise in PDEs. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18762503 URI : http://dx.doi.org/10.24350/CIRM.V.18762503 |
Bibliography
- Beck, L., Flandoli, F., Gubinelli, M., & Maurelli, M. (2014). Stochastic ODEs and stochastic linear PDEs with critical drift: regularity, duality and uniqueness.
- Catellier, R. (2015). Rough linear transport equation with an irregular drift.
- Catellier, R., & Gubinelli, M. (2014). Averaging along irregular curves and regularisation of ODEs.
- Chouk, K., & Gubinelli, M. (2015). Nonlinear PDEs with modulated dispersion I: Nonlinear Schrödinger equations.
- Chouk, K., & Gubinelli, M. (2014). Nonlinear PDEs with modulated dispersion II: Korteweg--de Vries equation.
