Preprint Article Version 1 This version is not peer-reviewed

# CONTINUITY AND MOTION (NAVIER-STOKES) EQUATIONS

Version 1 : Received: 19 August 2018 / Approved: 21 August 2018 / Online: 21 August 2018 (10:12:40 CEST)

How to cite: Provorov, D. CONTINUITY AND MOTION (NAVIER-STOKES) EQUATIONS. Preprints 2018, 2018080376 (doi: 10.20944/preprints201808.0376.v1). Provorov, D. CONTINUITY AND MOTION (NAVIER-STOKES) EQUATIONS. Preprints 2018, 2018080376 (doi: 10.20944/preprints201808.0376.v1).

## Abstract

The paper is considering of the basic differential equations of hydrodynamics: the equation of continuity and motion. On the simplest example, it is shown that the equation of continuity in a system with the equation of motion leads to contradictions and erroneous results of modeling. A more correct form of the continuity equation is described. It is shown that the equations of motion can be written in the form of complete differentials. Three possible integral forms of the equations of motion are presented. As a conclusion, the existence and smoothness of the solution of the Navier-Stokes equations are considered.

## Subject Areas

continuity equation, Navier-Stokes equation, Bernoulli equation, existence and smoothens of the solutions of Navier-Stokes equation
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