Abstract: The talk will present some recent results about the free boundary problem for an incompressible, irrotational liquid drop of nearly spherical shape with capillarity. The first part of the talk will deal with the extension of some classical results from the flat case to the spherical geometry, including the reduction to a problem on the boundary, the Hamiltonian structure, the analyticity and tame estimates for the Dirichlet-Neumann operator in Sobolev class, and a linearization formula for it, both by a differential geometry approach and with the method of the 'good unknown of Alinhac'. The second part of the talk will deal with the bifurcation of travelling waves, which are nontrivial fixed profiles rotating with constant angular velocity. Bifurcation from both simple and multiple eigenvalues is considered, where the Hamiltonian and variational structure of the problem, together with its conserved quantities, play a key role.
From works in collaboration with Vesa Julin, Domenico Angelo La Manna and Giuseppe La Scala.
Geometric analysis seminar: Pietro Baldi (University of Naples Federico II)
Event information
Event date
-
Event type
Public lectures, seminars and round tables
Event language
English
Event payment
Free of charge
Event location category
Mattilanniemi
