The Navier-Stokes equations for Incompressible Flows: solution properties at potential blow-up times

2015/03/05 by Lorenz, Jens, Zingano, Paulo R.
#35G20 #35Q30 #76D03 #76D05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/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.

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