  We consider the initial value problem for the inviscid Primitive and
Boussinesq equations in three spatial dimensions. We recast both systems as an
abstract Euler-type system and apply the methods of convex integration of De
Lellis and Sz\'ekelyhidi to show the existence of infinitely many global weak
solutions of the studied equations for general initial data. We also introduce
an appropriate notion of dissipative solutions and show the existence of
suitable initial data which generate infinitely many dissipative solutions.
