“On the existence of expansive solutions to the N-body problem”
Mercoledì 12 Marzo 2025, ore 13:00 - Aula 2AB40 - Davide Polimeni (Università di Torino)
Abstract
In this talk we deal, for the classical N-body problem, with the existence of action minimizing half entire expansive solutions with prescribed limit shape and initial configuration, tackling the cases of hyperbolic, parabolic and hyperbolic-parabolic arcs in a unified manner. Our approach is based on the minimization of a renormalized Lagrangian action defined on a suitable functional space. With this new strategy, we are able to confirm the already-known results of existence of both hyperbolic and parabolic solutions, and we prove for the first time the existence of hyperbolic-parabolic solutions for any prescribed asymptotic expansion in a suitable class. Associated with each element of this class, we find a viscosity solution of the Hamilton-Jacobi equation as a linear correction of the value function. Besides, we also manage to give a precise description of the growth of parabolic and hyperbolic-parabolic solutions.
This work is in collaboration with Susanna Terracini.
