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On the decay properties of solutions to the non-stationary Navier-Stokes equations in ℝ3

Published online by Cambridge University Press:  12 July 2007

Cheng He  and
Zhouping Xin
Cheng He
Affiliation:
Institute of Applied Mathematics, Academia Sinica, Beijing, 100080, People's Republic of China, and Institute of Mathematical Sciences, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong (cheng@math03.math.ac.cn)
Zhouping Xin
Affiliation:
Courant Institute, New York University, 251 Mercer Street, New York, NY 10012, USA, and Department of Mathematics and Institute of Mathematical Sciences, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong (zpxin@ims.cuhk.edu.hk)
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Abstract

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In this paper, we study the asymptotic decay properties in both spatial and temporal variables for a class of weak and strong solutions, by constructing the weak and strong solutions in corresponding weighted spaces. It is shown that, for the strong solution, the rate of temporal decay depends on the rate of spatial decay of the initial data. Such rates of decay are optimal.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 131 , Issue 3 , June 2001 , pp. 597 - 619
Copyright
Copyright © Royal Society of Edinburgh 2001