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Existence and Non-uniqueness of Global Weak Solutions to Inviscid Primitive and Boussinesq Equations

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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 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.

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Authors and Affiliations

  1. EPFL Lausanne, Station 8, 1015, Lausanne, Switzerland

    Elisabetta Chiodaroli

  2. Institute of Mathematics of the Czech Academy of Sciences, Žitná 25, 115 67, Prague 1, Czech Republic

    Martin Michálek

Authors
  1. Elisabetta Chiodaroli
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  2. Martin Michálek
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Correspondence to Elisabetta Chiodaroli.

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Communicated by W. Schlag

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Chiodaroli, E., Michálek, M. Existence and Non-uniqueness of Global Weak Solutions to Inviscid Primitive and Boussinesq Equations. Commun. Math. Phys. 353, 1201–1216 (2017). https://doi.org/10.1007/s00220-017-2846-5

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  • DOI: https://doi.org/10.1007/s00220-017-2846-5

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