Le equazioni di Eulero dal punto di vista delle inclusioni differenziali
Bollettino della Unione matematica italiana, Série 9, Tome 1 (2008) no. 3, pp. 873-879
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In a recent joint paper with L. Székelyhidi we have proposed 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.
De Lellis, Camillo. Le equazioni di Eulero dal punto di vista delle inclusioni differenziali. Bollettino della Unione matematica italiana, Série 9, Tome 1 (2008) no. 3, pp. 873-879. http://geodesic.mathdoc.fr/item/BUMI_2008_9_1_3_a16/
@article{BUMI_2008_9_1_3_a16,
author = {De Lellis, Camillo},
title = {Le equazioni di {Eulero} dal punto di vista delle inclusioni differenziali},
journal = {Bollettino della Unione matematica italiana},
pages = {873--879},
year = {2008},
volume = {Ser. 9, 1},
number = {3},
zbl = {1191.35212},
mrnumber = {2455350},
language = {it},
url = {http://geodesic.mathdoc.fr/item/BUMI_2008_9_1_3_a16/}
}