Improved stability for 2D attractive Bose gases

We study the ground-state energy of N attractive bosons in the plane. The interaction is scaled for the gas to be dilute so that the corresponding mean-field problem is a local non-linear Schrödinger (NLS) equation. We improve the conditions under which one can prove that the many-body problem is stable (of the second kind). This implies, using previous results, that the many-body ground states and dynamics converge to the NLS ones for an extended range of diluteness parameters.