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On the decay of higher-order norms of the solutions of Navier–Stokes equations

Published online by Cambridge University Press:  14 November 2011

Maria E. Schonbek  and
Michael Wiegner
Maria E. Schonbek
Affiliation:
Department of Mathematics, University of California, Santa Cruz, California 95064, U.S.A.
Michael Wiegner
Affiliation:
Department of Mathematics, University of Bayreuth, D-95440 Bayreuth, Germany
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Extract

We show that an energy decay ∥u(t)∥2 = O(t−µ) for solutions of the Navier–Stokes equations on ℝn, n ≦ 5, implies a decay of the higher order norms, e.g. ∥Dα u(t)∥2 = O(t−µ −|α|/2) and ∥u(t)|∞ = O(t−µ −n/4).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 3 , 1996 , pp. 677 - 685
Copyright
Copyright © Royal Society of Edinburgh 1996

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