Article
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A Conjecture on the Solution Existence of the Navier-Stokes Equation
Version 1
: Received: 8 July 2020 / Approved: 9 July 2020 / Online: 9 July 2020 (12:25:22 CEST)
How to cite: Sun, B. A Conjecture on the Solution Existence of the Navier-Stokes Equation. Preprints 2020, 2020070192. https://doi.org/10.20944/preprints202007.0192.v1 Sun, B. A Conjecture on the Solution Existence of the Navier-Stokes Equation. Preprints 2020, 2020070192. https://doi.org/10.20944/preprints202007.0192.v1
Abstract
For the solution existence condition of the Navier-Stokes equation, we propose a conjecture as follows: "\emph{The Navier-Stokes equation has a solution if and only if the determinant of flow velocity gradient is not zero, namely $\det (\bm \nabla \bm v)\neq 0$.}"
Keywords
solution existence condition; the Navier-Stokes equations; velocity gradient; tensor determinant
Subject
Physical Sciences, Fluids and Plasmas Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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