  The arrest of Langmuir-wave collapse by quantum effects, first addressed by
Haas and Shukla [Phys. Rev. E 79, 066402 (2009)] using a Rayleigh-Ritz
trial-function method is revisited, using rigorous estimates and systematic
asymptotic expansions. The absence of blow up for the so-called quantum
Zakharov equations is proved in two and three dimensions, whatever the strength
of the quantum effects. The time-periodic behavior of the solution for initial
conditions slightly in excess of the singularity threshold for the classical
problem is established for various settings in two space dimensions. The
difficulty of developing a consistent perturbative approach in three dimensions
is also discussed, and a semi-phenomenological model is suggested for this
case.
