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.