General Solution Theory for the Stochastic Navier-Stokes Equations
Event details
| Date | 08.02.2024 |
| Hour | 15:15 › 16:15 |
| Location |
Tukey room MA B1 504
|
| Category | Conferences - Seminars |
| Event Language | English |
Abstract: The Navier-Stokes Equations are the fundamental models for viscous fluid dynamics, but no prediction is perfect. Introducing randomness into differential equations has long been the answer to uncertainty quantification, inviting new methodologies for these stochastic perturbations to best refine our predictions. Recent developments in the modelling literature point to the significance oftransport noise, where the stochastic integral depends on the gradient of the solution; analytically, this unbounded noise breaks classical frameworks built for the study of nonlinear SPDEs.
In this talk, I shall present general well-posedness results for SPDEs with applications to the Navier-Stokes Equations under Stochastic Advection by Lie Transport. We consider three different solution types of increasing strength, applied for martingale weak, weak and strong solutions. Particular attention is given to the case of a physical boundary, where existence results for transport noise were previously unknown. I shall briefly comment on some inviscid limit results for the equations, and the prospect of a regularisation by noise phenomenon.
In this talk, I shall present general well-posedness results for SPDEs with applications to the Navier-Stokes Equations under Stochastic Advection by Lie Transport. We consider three different solution types of increasing strength, applied for martingale weak, weak and strong solutions. Particular attention is given to the case of a physical boundary, where existence results for transport noise were previously unknown. I shall briefly comment on some inviscid limit results for the equations, and the prospect of a regularisation by noise phenomenon.
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