A Note on L^2 Decay of Ladyzhenskaya Model

Abstract

This paper is concerned with time decay problem of Ladyzhenskaya model governed incompressible viscous fluid motion with the dissipative potential having p-growth (p ≥ 3) in R^3. With the aid of the spectral decomposition of the Stokes operator and L^p - L^q estimates, it is rigorously proved that the Leray-Hopf type weak solutions decay in L²(R^3) norm like t!n^{-\frac{n}{2}(\frac{1}{r}-\frac{1}{2}) under the initial data u_0 ∈ L²(R^3) ∩ L^r(R^3) for 1 ≤ r ‹ 2. Moreover, the explicit error estimates of the difference between Ladyzhenskaya model and Navier-Stokes flow are also investigated.