The rate of increase for recursion with quadratic non-linearity

TL;DR

This paper analyzes how quickly positive quadratic recursive sequences grow, focusing on their logarithmic growth rate, and discusses potential applications in Navier-Stokes theory.

Contribution

It provides a calculation of the logarithmic growth index for quadratic recursive sequences and explores their relevance to fluid dynamics.

Findings

Determined the growth rate of quadratic recursions.

Linked recursion growth to Navier-Stokes equations.

Proposed potential applications in fluid dynamics theory.

Abstract

We investigate in this short report the rate of increase of positive numerical recursion with quadratic non-linearity. More exactly, we intent to calculate the logarithmic index of its increasing. We present also the possible application in the theory of the Navier-Stokes equations.