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

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.

preprint2015arXivOpen access
Jens LorenzPaulo R. Zingano
math.AP
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Jens LorenzPaulo R. Zingano

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