Differential and Integral Equations

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

Utpal Manna and S. S. Sritharan

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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

Permanent link to this document
https://projecteuclid.org/euclid.die/1356039440

Mathematical Reviews number (MathSciNet)
MR2324217

Zentralblatt MATH identifier
1212.35367

Subjects
Primary: 35Q35: PDEs in connection with fluid mechanics
Secondary: 76D03: Existence, uniqueness, and regularity theory [See also 35Q30] 76D05: Navier-Stokes equations [See also 35Q30]

Citation

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.


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