Speaker
Description
In this talk, we will present the rigorous proof of existence of ground states for the Schrödinger-Poisson system, which model rotating boson stars. The model reduces to minimizing an energy functional under an ansatz with $SO(2)$ symmetry.
The main analytical challenge is the loss of compactness typical of Sobolev embeddings in $\mathbb{R}^3$. Using the concentration-compactness principle, we will show how the structure of the variational problem overcomes this obstacle: on the one hand, axial symmetry prevents the radial leakage of mass; on the other, the energy functional is strictly sub-additive, forbidding fragmentation. With this, we guarantee the pre-compactness of the minimizing sequences and the existence of the star. To conclude, we will briefly outline how this variational framework allows us to deduce the orbital stability of these solutions.