  There is renewed interest in the question of whether the Navier-Stokes
equations (NSE), one of the fundamental models of classical physics and widely
used in engineering applications, are actually self-consistent. After recalling
the essential physical assumptions inherent in the NSE, the notion of weak
solutions, possible implications for the energy conservation law, as well as
existence and uniqueness in the incompressible case are discussed. Emphasis
will be placed on the possibility of finite time singularities and their
consequences for length scales which should be consistent with the continuum
hypothesis.
