Detalles de Evento
Title: Existence of compactly supported global minimisers for the interaction energy
Speaker: Francesco Patacchini, Imperial College (UK)
Abstract: We show the existence of compactly supported global minimisers under almost optimal hypotheses for continuum models of particles interacting through a potential. The main assumption on the potential is that it is catastrophic, or not H-stable, which is the complementary assumption to that in classical results on thermodynamic limits in statistical mechanics. The proof is based on a uniform control on the local mass around each point of the support of a global minimiser, together with an estimate on the size of the ``gaps'' it may have. The class of potentials for which we prove existence of global minimisers includes power-law potentials and, for some range of parameters, Morse potentials, widely used in applications. This is a joint work with J. A. Cañizo and J. A. Carrillo.
1 de octubre, 12:30, Seminario 1ª planta IEMath-GR
More information about the Differential Equations Seminar here.
Speaker: Francesco Patacchini, Imperial College (UK)
Abstract: We show the existence of compactly supported global minimisers under almost optimal hypotheses for continuum models of particles interacting through a potential. The main assumption on the potential is that it is catastrophic, or not H-stable, which is the complementary assumption to that in classical results on thermodynamic limits in statistical mechanics. The proof is based on a uniform control on the local mass around each point of the support of a global minimiser, together with an estimate on the size of the ``gaps'' it may have. The class of potentials for which we prove existence of global minimisers includes power-law potentials and, for some range of parameters, Morse potentials, widely used in applications. This is a joint work with J. A. Cañizo and J. A. Carrillo.
1 de octubre, 12:30, Seminario 1ª planta IEMath-GR
More information about the Differential Equations Seminar here.
