an:01309486
Zbl 0941.35066
Takahashi, Shuji
A weighted equation approach to decay rate estimates for the Navier-Stokes equations
EN
Nonlinear Anal., Theory Methods Appl. 37, No. 6, A, 751-789 (1999).
00057588
1999
j
35Q30 35B40
regularity class; optimal decay rates in space-time; nonstationary incompressible Navier-Stokes equation
The nonstationary incompressible Navier-Stokes equation in \({\mathbb R}^n (n\geq 2)\) is considered. The goal of this paper is to show almost optimal uniform decay estimates (i.e., almost the same decay rate estimates as those for heat equations), for weak solutions of the Navier-Stokes equation in the class \(L^s(0, \infty; L^q({\mathbb R}^n)^n)\) with \(n/q+2/s=1\) and \(\|u\|_{q,s}\ll 1\), under prescribed decay rates of external forces. The decay rates of the solution and complete proofs are given.
O.Dementev (Chelyabinsk)