Calculus of Variations and Geometric Measure Theory

C. De Lellis

Le equazioni di Eulero dal punto di vista delle inclusioni differenziali

created by delellis on 12 Apr 2026

[BibTeX]

Published Paper

Inserted: 12 apr 2026
Last Updated: 12 apr 2026

Journal: Boll. Unione Mat. Ital. (9)
Volume: 1
Number: 3
Pages: 873-879
Year: 2008

Abstract:

In a recent joint paper with L. Sz\'ek\'elyhidi we have proposed a new point of view on weak solutions of the Euler equations, describing the motion of an ideal incompressible fluid in $R^n$ 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.


Download: