[Seminar] "Normalized solutions and limit profiles of the Gross-Pitaevskii-Poisson equation" by Prof. Vitaly Moroz

Geometric PDE and Applied Analysis Seminar (January 14, 2026)

Title: Normalized solutions and limit profiles of the Gross-Pitaevskii-Poisson equation

Speaker: Prof. Vitaly Moroz (Swansea University)

Abstract: Gross-Pitaevskii-Poisson (GPP) equation is a nonlocal modification of the Gross-Pitaevskii equation with an attractive Coulomb-like term. It appears in the models of self-gravitating Bose-Einstein condensates proposed in cosmology and astrophysics to describe Cold Dark Matter and Boson Stars. We investigate the existence of prescribed mass (normalised) solutions to the GPP equation, paying special attention to the shape and asymptotic behaviour of the associated mass-energy relation curves and to the limit profiles of solutions at the endpoints of these curves. In particular, we show that after appropriate rescalings, the constructed normalized solutions converge either to a ground state of the Choquard equation, or to a compactly supported radial ground state of the integral Thomas-Fermi equation. In different regimes the constructed solutions include global minima, local but not global minima and unstable mountain-pass type solutions. This is a joint work with Riccardo Molle (Rome Tor Vergata) and Giuseppe Riey (Calabria).