Calculus of Variations and Geometric Measure Theory

E. Chiodaroli - M. Michalek

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

created by chiodaroli on 08 Sep 2016
modified on 09 Sep 2016



Inserted: 8 sep 2016
Last Updated: 9 sep 2016

Year: 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.