Stability of attractive 3D Bose gases with repulsive three-body interactions

We consider three-dimensional Bose gases with attractive two-body interactions and repulsive three-body interactions. We prove the stability of the second kind of the system for a large class of interaction potentials and scaling regimes, which includes the Gross--Pitaevskii regime for the three-body potential. In addition, we even prove the classical stability of the system for a more restrictive class of interactions and scaling regimes. The main ingredient of the proof is a bound that was derived recently in a study by the authors on the dynamics of Bose gases with three-body interactions in the Gross--Pitaevskii regime (2026).