Abstract: 
In this paper I prove that any flowsolution of the NavierStokes equations ,
under standard assumption of the official formulation of the 4th Clay millennium
problem, has a secondary potential flow , with different velocities and pressures but
identical spacetime evolution of the matrix of deformations. In this way we can
reduce the global in time behaviour of the original flowsolution to the one of the
potential flow and solve the 4th Clay millennium problem. But I solve also a by far
more difficult problem as I prove the same thing for the inviscid flows of the Euler
equations.
