General solution of the Navier-Stokes system, as parameter function and its geophysic and gydroaerodinamic practice

TL;DR

This paper presents a unique parametric solution to the Navier-Stokes equations that models fluid velocity and density, with applications in geophysics, aerodynamics, and natural disaster analysis.

Contribution

It introduces a novel parametric approach to solving Navier-Stokes equations, linking fluid dynamics to geophysical and aeronautical phenomena.

Findings

Solution is unique and smooth.

Defines conditions for turbulence and shock waves.

Connects fluid dynamics to earthquake and volcanic activity.

Abstract

We consider the Navier-Stokes system solution, based at parametric representation of desired function. This solution is unique and it show the velocity of a stream element as its density structure [{\rho}_S (x,y,z,t);{\rho}^\to_L (x,y,z,t)] function. The solution is smooth, defining conditions of turbulence occurrence and supersonic shock waves in the viscous substance. Given solution brings to light the genesis of earthquakes and volcanic activity, of turbulence phenomenon and possible stave off natural and anthropogenic catastrophes, connecting with this effect. Given solution allows to evaluate the Bernoulli's law {\guillemotleft}line density{\guillemotright} mechanism for aerodynamical airplanes checkouts and hydromechanical tests correlation, for high-speed extension flood river compensation. In addition given function allows to apply {\guillemotleft}isostatic breakdown{\guillemotright} mechanism for resolution of the Gulf of Mexico and similar problem.