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.
Citation
Utpal Manna. S. S. Sritharan. "Lyapunov functionals and local dissipativity for the vorticity equation in $L^p$ and Besov spaces." Differential Integral Equations 20 (5) 481 - 498, 2007. https://doi.org/10.57262/die/1356039440
Information