## Differential and Integral Equations

### Lyapunov functionals and local dissipativity for the vorticity equation in $L^p$ and Besov spaces

#### Abstract

In this paper we establish the local Lyapunov property of certain $\mathrm{L}^{p}$ and Besov norms of the vorticity fields. We have resolved in part, a certain open problem posed by Tosio Kato for the three-dimensional Navier-Stokes equation by studying the vorticity equation. The local dissipativity of the sum of linear and non-linear operators of the vorticity equation is established. One of the main techniques used here is Littlewood-Paley analysis.

#### Article information

Source
Differential Integral Equations, Volume 20, Number 5 (2007), 481-498.

Dates
First available in Project Euclid: 20 December 2012

Manna, Utpal; Sritharan, S. S. Lyapunov functionals and local dissipativity for the vorticity equation in $L^p$ and Besov spaces. Differential Integral Equations 20 (2007), no. 5, 481--498. https://projecteuclid.org/euclid.die/1356039440