Remarks on unsolved basic problems of the Navier-Stokes equations

Details Remarks on unsolved basic problems of the Navier-Stokes equations Remarks on unsolved basic problems of the Navier-Stokes equations

2001-01-04

arxiv.org/abs/physics/0101027v1

Nonlinear Phenomena in Complex Systems, 2:3 (1999) 32-37

Physics

Fluid Dynamics

Lecture given at 3rd International Summer School/Conference, Let's face chaos through nonlinear dynamics, Maribor, Slovenia, 2

Scientific paper

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.

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