Existence of weak solutions for the incompressible Euler equations
Annales de l'I.H.P. Analyse non linéaire, Volume 28 (2011) no. 5, p. 727-730

Using a recent result of C. De Lellis and L. Székelyhidi Jr. (2010) [2] we show that, in the case of periodic boundary conditions and for arbitrary space dimension $d⩾2$, there exist infinitely many global weak solutions to the incompressible Euler equations with initial data ${v}_{0}$, where ${v}_{0}$ may be any solenoidal ${L}^{2}$-vectorfield. In addition, the energy of these solutions is bounded in time.

@article{AIHPC_2011__28_5_727_0,
author = {Wiedemann, Emil},
title = {Existence of weak solutions for the incompressible Euler equations},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
publisher = {Elsevier},
volume = {28},
number = {5},
year = {2011},
pages = {727-730},
doi = {10.1016/j.anihpc.2011.05.002},
zbl = {1228.35172},
mrnumber = {2838398},
language = {en},
url = {http://www.numdam.org/item/AIHPC_2011__28_5_727_0}
}

Wiedemann, Emil. Existence of weak solutions for the incompressible Euler equations. Annales de l'I.H.P. Analyse non linéaire, Volume 28 (2011) no. 5, pp. 727-730. doi : 10.1016/j.anihpc.2011.05.002. http://www.numdam.org/item/AIHPC_2011__28_5_727_0/

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[4] László Székelyhidi, Emil Wiedemann, Generalised Young measures generated by ideal incompressible fluid flows, arXiv:1101.3499 (2011) | MR 2968597 | Zbl 1256.35072