Remarks on backward uniqueness of parabolic equations and incompressible Navier-Stokes well-posedness

F. Lam

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arXiv · 1509.04940

Remarks on backward uniqueness of parabolic equations and incompressible Navier-Stokes well-posedness

F. Lam

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Abstract

We explain why the theory of Escauriaza, Seregin, and Sverak (Russian Math. Surveys, 2003) on potential finite time singularity in Navier-Stokes solutions must be largely misapprehended. It is found that the proofs of the backward uniqueness theorem for parabolic equations contain technical errors. The stated validity of a theorem for vorticity is established on ill-informed analyses as the solenoidal constraint is not taken into account. There are many cases where parabolic scalings are erroneously applied. We briefly discuss a number of related issues.

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F. Lam. 2015-09-16. Remarks on backward uniqueness of parabolic equations and incompressible Navier-Stokes well-posedness. https://arxiv.org/abs/1509.04940

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