STAR-seminars: Dan Crisan

Image may contain: Sky, Architecture, Animation.

The webinars will take place on Zoom and a link to the virtual room will be sent out to all those who registered at the registration page.

-----------------------------------------------------------

Speaker: Dan Crisan - Imperial College London

Title: Well-posedness Properties for a Stochastic Rotating Shallow Water Model 

Abstract: The rotating shallow water (RSW) equations describe the evolution of a compressible rotating fluid below a free surface. The typical vertical length scale is assumed to be much smaller than the horizontal one, hence the shallow aspect. The RSW equations are a simplification of the primitive equations which are the equations of choice for modelling atmospheric and oceanic dynamics. In this talk, I will present some  well-posedness properties of a viscous rotating shallow water system. The system is stochastically perturbed in such a way that two key properties of its deterministic counterpart are preserved. First, it retains the characterisation of its dynamics as the critical path of a variational problem. In this case, the corresponding action function is stochastically perturbed. Secondly, it satisfies the classical Kelvin circulation theorem.  The introduction of stochasticity replaces the effects of the unresolved scales.  The stochastic RSW equations are shown to admit a unique maximal strong solution in a suitably chosen Sobolev space which depends continuously on the initial datum. The maximal stopping time up to which the solution exist is shown to be strictly positive and,  for sufficiently small initial datum, the solution is shown global in time with positive probability. This is joint work with Dr Oana Lang (Imperial College London) and forms part of the ERC Synergy project “Stochastic transport in upper ocean dynamics” (https://www.imperial.ac.uk/ocean-dynamics-synergy/)

---------------------------------------------------------

This series of webinars addresses all interested people in probability, stochastic analysis, control, risk evaluation, statistics, with a view towards applications, in particular to renewable energy markets and production. This series brings together the major research themes of the projects STORMSCROLLER, and SPATUS

Published Apr. 7, 2021 12:51 PM - Last modified Apr. 30, 2021 5:37 PM