SDEs and linear SPDEs with rough coefficients arising from fluid dynamics
Event details
| Date | 29.03.2012 |
| Hour | 10:15 › 11:15 |
| Speaker | Mario Maurelli |
| Location | |
| Category | Conferences - Seminars |
In this talk I will consider the problem of pathwise uniqueness for stochastic continuity equations (SCEs) and similar equations, in the case of rough coefficients. The SCE represents the evolution of a mass driven by the associated SDE and therefore is useful to capture regularization-by-noise phenomena and splitting/coalescence behaviour of the mass. I will state the classical rigorous link between an ODE and the associated continuity equation (superposition principle), its generalization for an additive noise and the consequences of this link ([1], [2]). Then, I will show Le Jan's theory, which uses Wiener chaos decomposition and selects a unique Wiener generalized solution to a SCE ([3]). This is suitable for models arising in fluid dynamics, in cases of non strong uniqueness, but can also be applied to restore uniqueness, starting from an ill-posed linear PDE ([4]). Further research directions will be mentioned.
Practical information
- General public
- Free
Organizer
- CIB
Contact
- Isabelle Derivaz-Rabii