Pushing the Boundaries of Stochastic Fluid Dynamics
A talk in the SPDEvent series by
Daniel Goodair from Imperial College London
| Abstract: | From the theoretical perspective, the recent introduction of transport noise into fluid dynamics models invites two interesting questions: do we retain the analytical properties of the deterministic equations for a wide class of such noise, and can we improve upon these properties for a specific choice of noise within the class. My talk will be focused on the former, with a brief eye to the latter. In particular, I will discuss the existence of solutions in the presence of a physical boundary. This will be guided by recent difficulties and successes surrounding the Navier-Stokes Equation with Stochastic Lie Transport, addressing the challenges arising in a bounded domain and what standard techniques can and cannot cope with. The critical result is that whilst the existence of strong solutions under the no-slip boundary condition remains unobtained, we can achieve solutions under the seemingly more challenging Navier boundary conditions. |