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Acta Applicandae Mathematica

, Volume 37, Issue 1–2, pp 215–219 | Cite as

Decay of the L-norm of solutions of Navier-Stokes equations in unbounded domains

  • Michael Wiegner
Article

Abstract

We show that for nn⩽ 4 the L-norm of weak solutions of the Navier-Stokes equations on ℝn with generalized energy inequality decays like\(\parallel u(t, \cdot )\parallel _\infty = O(t^{ - ({{n + 1)} \mathord{\left/ {\vphantom {{n + 1)} 2}} \right. \kern-\nulldelimiterspace} 2}} ),if(1 + | \cdot |)|u(0, \cdot )| \in L_1 \) and
$$\int_{\mathbb{R}^n } {u(0,x)} dx = 0$$
.

The same holds for strong solutions in all dimensions, if additionally u(0, ·) ε Lpp >n.

Mathematics subject classifications (1991)

35Q30 35B40 

Key words

time decay Navier-Stokes equations 

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Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Michael Wiegner
    • 1
  1. 1.Mathematisches Institut der UniversitÄtUniversitÄt BayreuthBayreutkGermany

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