Existence of weak solutions for the incompressible Euler equations

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 v0, where v0 may be any solenoidal L2-vectorfield. In addition, the energy of these solutions is bounded in time.