The Navier-Stokes equations for Incompressible Flows: solution properties at potential blow-up times
arXiv:1503.01767
Abstract
In this paper we consider the Cauchy problem for the 3D Navier-Stokes equations for incompressible flows. The initial data are assumed to be smooth and rapidly decaying at infinity. A famous open problem is whether classical solutions can develop singularities in finite time. Assuming the maximum interval of existence to be finite, we give a unified discussion of various known solution properties as time approaches the blow-up time.
Unpublished Report, Universidade Federal do Rio Grande do Sul, 2002