Seminarium KMMF "Teoria Dwoistości"

Different Poisson structures have been proposed to give a Hamiltonianformulation to evolution equations issued from fluid mechanics. In thistalk, I will investigate the main brackets which appear in theliterature and discuss the difficulties which arise when one tries togive a rigorous meaning to these brackets. In the first part of my talk,I will recall basic material on Poisson brackets on a finite dimensionalmanifold and present the difficulties which arise when one extend theseconcepts to infinite dimensional manifolds. In the second part of mytalk, I will focus on the problem of defining a valid and usable bracketto study rotational fluid flows with a free boundary. I will discusssome results which have emerged in the literature to solve thedifficulties which arise and conclude that (up to my knowledge) the mainproblems are still open.To attend our online seminar please use the Zoom identificator:https://us02web.zoom.us/j/8145917621?pwd=bVVKend0SHFKNUNyUUQ4cWNRK3laZz09