Tetsuro Miyakawa, Department of Mathematics, Kobe University, Rokko, Kobe 657-8501, Japan, e-mail: miyakawa@math.kobe-u.ac.jp; Maria Elena Schonbek, Department of Mathematics, University of California, Santa Cruz, CA 95064, USA, e-mail: schonbek@math.ucsc.edu
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 (MSC 2000): 35Q10
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