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We consider the initial value problem for the inviscid Primitive andBoussinesq equations in three spatial dimensions. We recast both systems as anabstract Euler-type system and apply the methods of convex integration of DeLellis and Sz\'ekelyhidi to show the existence of infinitely many global weaksolutions of the studied equations for general initial data. We also introducean appropriate notion of dissipative solutions and show the existence ofsuitable initial data which generate infinitely many dissipative solutions.

Existence and non-uniqueness of global weak solutions to inviscid primitive and Boussinesq equations