  We define the concept of energy-variational solutions for the Navier--Stokes
and Euler equations. This concept is shown to be equivalent to weak solutions
with energy conservation. Via a standard Galerkin discretization, we prove the
existence of energy-variational solutions and thus weak solutions in any space
dimension for the Navier--Stokes equations. In the limit of vanishing viscosity
the same assertions are deduced for the incompressible Euler system. Via the
selection criterion of maximal dissipation we deduce well-posedness for these
equations.
