## Advances in Differential Equations

### On the boundedness and decay of moments of solutions to the Navier-Stokes equations

#### Abstract

In this paper we consider the existence and decay of moments of the solutions to the Navier-Stokes equations in the whole space ${{\bf R}^n}$; $n \geq 2$ for existence, $2 \leq n \leq 5$ for decay. The decay obtained is algebraic, of order $\int_{{{\bf R}^n}} |x|^k |u|^2\,dx \leq C(t+1)^{-2\mu(1-k/n)}$ for $0\leq k\leq n$, for solutions $u$ of appropriate data for which the $L^2$ norm decays at a rate of order $\mu$. That is for solutions that satisfy $||u(t)||_2 \leq C(t+1) ^{-\mu}$. Where $\mu >1/2$. Such solutions are easy to obtain as for example it suffices for $n=3$ that the data $u_0$ is in $L^2 \cap L^1$.

#### Article information

Source
Adv. Differential Equations, Volume 5, Number 7-9 (2000), 861-898.

Dates
First available in Project Euclid: 27 December 2012

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