Using a recent result of C. De Lellis and L. Székelyhidi Jr. (2010)  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.
Cite this article
Emil Wiedemann, Existence of weak solutions for the incompressible Euler equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 28 (2011), no. 5, pp. 727–730DOI 10.1016/J.ANIHPC.2011.05.002