On a nonlinear recurrent relation

We study the limiting behavior for the solutions of a nonlinear recurrent relation which arises from the study of Navier-Stokes equations. Some stability theorems are also shown concerning a related class of linear recurrent relations.Comment: to appear in Journal of Statistical Physic

Separating Solution of a Quadratic Recurrent Equation

In this paper we consider the recurrent equation $$\Lambda_{p+1}=\frac1p\sum_{q=1}^pf\bigg(\frac{q}{p+1}\bigg)\Lambda_{q}\Lambda_{p+1-q}$$ for $p\ge 1$ with $f\in C[0,1]$ and $\Lambda_1=y>0$ given. We give conditions on $f$ that guarantee the existence of $y^{(0)}$ such that the sequence $\Lambda_p$ with $\Lambda_1=y^{(0)}$ tends to a finite positive limit as $p\to \infty$.Comment: 13 pages, 6 figures, submitted to J. Stat. Phy