Existence and non-uniqueness of global weak solutions to inviscid primitive and Boussinesq equations
Analysis of PDEs
2017-04-05 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1609.02444,
title = {Existence and non-uniqueness of global weak solutions to inviscid primitive and Boussinesq equations},
author = {Elisabetta Chiodaroli and Martin Michálek},
journal= {arXiv preprint arXiv:1609.02444},
year = {2017}
}