Finite time singularity formation for a nonlocal Boussinesq system arising in cold-plasma dynamics

We study finite-time singularity formation for a nonlocal Boussinesq system arising in cold-plasma dynamics. We show that smooth, symmetric initial data with strictly positive total density and a sufficiently negative velocity slope at the origin lead to finite-time blow-up. More precisely, we give an explicit upper bound for the lifespan and show that the velocity gradient becomes unbounded.