Abstract
It is proved that if the Navier-Stokes problem is considered in ℝ3, then the initial velocity has to be zero. This is the paradox. The consequences of this paradox are: a) The NSP is contradictory physically and mathematically; it is not a correct formulation of the problem of motion of the incompressible viscous fluid. b) The solution to the NSP does not exist on [0, ∞). This solves one of the millennium problems.
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