  The 2D conservative Boussinesq system describes inviscid, incompressible,
buoyant fluid flow in gravity field. The possibility of finite time blow up for
solutions of this system is a classical problem of mathematical hydrodynamics.
We consider a 1D model of 2D Boussinesq system motivated by a particular finite
time blow up scenario. We prove that finite time blow up is possible for the
solutions to the model system.
