Existence of weak solutions for the incompressible Euler equations
Annales de l'I.H.P. Analyse non linéaire, Tome 28 (2011) no. 5, pp. 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 , there exist infinitely many global weak solutions to the incompressible Euler equations with initial data , where may be any solenoidal -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},
pages = {727--730},
year = {2011},
publisher = {Elsevier},
volume = {28},
number = {5},
doi = {10.1016/j.anihpc.2011.05.002},
mrnumber = {2838398},
zbl = {1228.35172},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2011.05.002/}
}
TY - JOUR AU - Wiedemann, Emil TI - Existence of weak solutions for the incompressible Euler equations JO - Annales de l'I.H.P. Analyse non linéaire PY - 2011 SP - 727 EP - 730 VL - 28 IS - 5 PB - Elsevier UR - http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2011.05.002/ DO - 10.1016/j.anihpc.2011.05.002 LA - en ID - AIHPC_2011__28_5_727_0 ER -
%0 Journal Article %A Wiedemann, Emil %T Existence of weak solutions for the incompressible Euler equations %J Annales de l'I.H.P. Analyse non linéaire %D 2011 %P 727-730 %V 28 %N 5 %I Elsevier %U http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2011.05.002/ %R 10.1016/j.anihpc.2011.05.002 %G en %F 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, Tome 28 (2011) no. 5, pp. 727-730. doi: 10.1016/j.anihpc.2011.05.002
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