This seminar will be presented in hybrid mode.  The speaker will deliver her talk in person.

Title: On pathwise maximal solutions for stochastic shallow water models

Abstract: In this talk I will present the analytical properties of a stochastic shallow water model which has been derived using the Stochastic Advection by Lie Transport (Holm, 2015) approach. The unique maximal solution is proven to be strong and we provide sufficient conditions under which it is global with positive probability. Our approach is based on constructing a local solution using a linearised version of the original model and reducing the problem of global existence to a blow-up problem for one-dimensional SDEs. I will then compare this method with a more straightforward one which relies on a different approximating sequence which satisfies a Cauchy property. We use this latter procedure to show well-posedness for a different stochastic shallow water model which has been derived using the Location Uncertainty (Mémin, 2014) approach. The talk is partially based on this paper: https://arxiv.org/abs/2107.06601. 

The talk will be followed by refreshments in the Huxley Common Room at 5pm.