no. 5
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 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.

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     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},
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     number = {5},
     doi = {10.1016/j.anihpc.2011.05.002},
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     zbl = {1228.35172},
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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

[1] Peter Constantin, Ciprian Foias, Navier–Stokes Equations, Chicago Lectures in Math., The University of Chicago Press, Chicago (1988) | MR | Zbl

[2] Camillo De Lellis, László Székelyhidi, On admissibility criteria for weak solutions of the Euler equations, Arch. Ration. Mech. Anal. 195 no. 1 (2010), 225-260 | MR | Zbl

[3] Jean Leray, Sur le mouvement dʼun liquide visqueux emplissant lʼespace, Acta Math. 63 no. 1 (1934), 193-248 | MR

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

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