Stability of the two-dimensional Bose gases in the resonant regime

We consider a two-dimensional Bose gas formed in a planar atomic trap in conditions where the two-dimensional scattering length exceeds all other microscopic length scales in the system and, accordingly, the gas parameter assumes relatively high values. We show that, unlike in the three-dimensional case, for sufficiently low areal densities the two-dimensional gas remains stable against collapse even in the resonant regime. Furthermore, we evaluate the three-body recombination rate that sets the upper limit for the life-time of two-dimensional resonant atomic condensate.