MATHEMATICA BOHEMICA, Vol. 126, No. 2, pp. 443-455 (2001)

On optimal decay rates for weak solutions to the Navier-Stokes equations in $\bb R^n$

Tetsuro Miyakawa, Maria Elena Schonbek

Tetsuro Miyakawa, Department of Mathematics, Kobe University, Rokko, Kobe 657-8501, Japan, e-mail:; Maria Elena Schonbek, Department of Mathematics, University of California, Santa Cruz, CA 95064, USA, e-mail:

Abstract: This paper is concerned with optimal lower bounds of decay rates for solutions to the Navier-Stokes equations in $\Bbb R^n$. Necessary and sufficient conditions are given such that the corresponding Navier-Stokes solutions are shown to satisfy the algebraic bound $$ \Vert u(t) \Vert \ge (t+1)^{-\frac {n+4}{2}}. $$

Keywords: decay rates, Navier-Stokes equations

Classification (MSC2000): 35Q10

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