  We introduce the new concept of maximal dissipative solutions for a general
class of isothermal GENERIC systems. Under certain assumption, we show that
maximal dissipative solutions are well posed as long as the bigger class of
dissipative solutions is non-empty. Applying this result to the Navier--Stokes
and Euler equations, we infer global well-posedness of maximal dissipative
solutions for these systems. The concept of maximal dissipative solutions
coincides with the concept of weak solutions as long as the weak solutions
inherits enough regularity to be unique.
