Geodesic
The Euler equations as a differential inclusion
Camillo De Lellis1 ; László Székelyhidi Jr.2
1 Institut für Mathematik<br/>Universität Zürich<br/>CH-8057 Zürich<br/>Switzerland
2 Departement Mathematik<br/>ETH Zürich<br/>CH-8092 Zürich<br/>Switzerland
Annals of mathematics, Tome 170 (2009) no. 3, pp. 1417-1436.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We propose a new point of view on weak solutions of the Euler equations, describing the motion of an ideal incompressible fluid in $\mathbb{R}^n$ with $n\geq 2$. We give a reformulation of the Euler equations as a differential inclusion, and in this way we obtain transparent proofs of several celebrated results of V. Scheffer and A. Shnirelman concerning the non-uniqueness of weak solutions and the existence of energy-decreasing solutions. Our results are stronger because they work in any dimension and yield bounded velocity and pressure.
DOI : 10.4007/annals.2009.170.1417

Camillo De Lellis 1 ; László Székelyhidi Jr. 2

1 Institut für Mathematik<br/>Universität Zürich<br/>CH-8057 Zürich<br/>Switzerland
2 Departement Mathematik<br/>ETH Zürich<br/>CH-8092 Zürich<br/>Switzerland 
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Camillo De Lellis; László Székelyhidi Jr. The Euler equations as a differential inclusion. Annals of mathematics, Tome 170 (2009) no. 3, pp. 1417-1436. doi : 10.4007/annals.2009.170.1417. http://geodesic.mathdoc.fr/articles/10.4007/annals.2009.170.1417/

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