An Alternative Resolution of the Navier–Stokes Problem through Zeno’s Arrow Paradox

The classical Navier–Stokes existence and smoothness problem pre- supposes a continuous time parameter. This assumption parallels Zeno’s paradox of the “flying arrow,” where infinite divisibility of time renders motion paradoxical. In this paper, we argue that the reliance on a continuous temporal axis makes the smoothness prob- lem ill-posed. By rejecting infinite divisibility and adopting a discrete or probabilistic conception of time, the paradox dissolves. Thus, the “existence and smoothness problem” is not to be solved within clas- sical analysis, but to be dissolved by a reformulation of temporal ontology.