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2007 Lyapunov functionals and local dissipativity for the vorticity equation in $L^p$ and Besov spaces
Utpal Manna, S. S. Sritharan
Differential Integral Equations 20(5): 481-498 (2007).

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

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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.

Information

Published: 2007
First available in Project Euclid: 20 December 2012

zbMATH: 1212.35367
MathSciNet: MR2324217

Subjects:
Primary: 35Q35
Secondary: 76D03 , 76D05

Rights: Copyright © 2007 Khayyam Publishing, Inc.

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Vol.20 • No. 5 • 2007
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