De Lellis, Camillo:
Le equazioni di Eulero dal punto di vista delle inclusioni differenziali
Bollettino dell'Unione Matematica Italiana Serie 9 1 (2008), fasc. n.3, p. 873-879, (Italian)
pdf (384 Kb), djvu (77 Kb). | MR 2455350 | Zbl 1191.35212
Sunto
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.
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