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EnglishWe 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 Szekelyhidi 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.
| Autori interni: | |
| Autori: | Chiodaroli, Elisabetta; Michalek, Martin |
| Titolo: | Existence and Non-uniqueness of Global Weak Solutions to Inviscid Primitive and Boussinesq Equations |
| Anno del prodotto: | 2017 |
| 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 Szekelyhidi 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. |
| Digital Object Identifier (DOI): | 10.1007/s00220-017-2846-5 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
File in questo prodotto:
| File | Descrizione | Tipologia | Licenza | |
|---|---|---|---|---|
| 1609.02444.pdf | Versione post-print | Documento in Post-print | Tutti i diritti riservati (All rights reserved) | Open AccessVisualizza/Apri |
http://hdl.handle.net/11568/872532
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