  A new construction technique of multiple solutions of the Euler equa- tion in
strong spaces is introduced which reveals the relationship to multi- ple Navier
Stokes equation solutions with special force terms while avoid- ing viscosity
limit constructions. This shows that severe restrictions have to be imposed on
time dependent external force terms in order to ob- tain uniqueness for the
Navier Stokes equation Cauchy problem. Such restrictions are imposed in the
statement of the so-called millenium prob- lem. Minimal turbulence models
should arguably incorporate weaker force terms in order to account for boundary
conditions and forces. However, we show that models of this type which have
been proposed recently, do not have a unique solution. This lack of determinism
of mimimal turbu- lence models indicates a dilemma: either models are too
simple to capture turbulence but may have unique smooth solutions, or there is
a modelling gap as the model does not determine a unique solution.
