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 d2, 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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