Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# 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 (doi: 10.20944/preprints202007.0192.v1). Sun, B. A Conjecture on the Solution Existence of the Navier-Stokes Equation. Preprints 2020, 2020070192 (doi: 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 $\det (\bm \nabla \bm v)\neq 0$.}"

## Subject Areas

solution existence condition; the Navier-Stokes equations; velocity gradient; tensor determinant

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