Inserted: 8 sep 2016
Last Updated: 9 sep 2016
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 Székelyhidi 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.