BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Dan Crisan (Imperial College London) DTSTART:20210601T090000Z DTEND:20210601T100000Z DTSTAMP:20260423T005737Z UID:SPDEs/3 DESCRIPTION:Title: We ll-posedness Properties for a Stochastic Rotating Shallow Water Model\ nby Dan Crisan (Imperial College London) as part of Stochastic PDEs and th eir friends\n\n\nAbstract\nThe rotating shallow water (RSW) equations desc ribe the evolution of a compressible rotating fluid below a free surface. The typical vertical length scale is assumed to be much smaller than the h orizontal one\, hence the shallow aspect. The RSW equations are a simplifi cation of the primitive equations which are the equations of choice for mo delling atmospheric and oceanic dynamics. In this talk\, I will present so me well-posedness properties of a viscous rotating shallow water system. T he system is stochastically perturbed in such a way that two key propertie s of its deterministic counterpart are preserved. First\, it retains the c haracterisation of its dynamics as the critical path of a variational prob lem. In this case\, the corresponding action function is stochastically pe rturbed. 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 s trong solution in a suitably chosen Sobolev space which depends continuous ly on the initial datum. The maximal stopping time up to which the solutio n exist is shown to be strictly positive and\, for sufficiently small init ial datum\, the solution is shown global in time with positive probability . This is joint work with Dr Oana Lang (Imperial College London).\n LOCATION:https://researchseminars.org/talk/SPDEs/3/ END:VEVENT END:VCALENDAR