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arXiv:0802.2898 [math.AP]AbstractReferencesReviewsResources

Lyapunov Functionals and Local Dissipativity for the Vorticity Equation in L^p and Besov Spaces

Utpal Manna, Sivaguru S. Sritharan

Published 2008-02-20Version 1

In this paper we establish the local Lyapunov property of certain 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.

Comments: 18 pages
Journal: Differential and Integral Equations, Volume20, Number 5 (2007), 481- 498
Categories: math.AP
Subjects: 35Q35, 47H06, 76D03, 76D05
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