A Note on L^2 Decay of Ladyzhenskaya Model (Journal of Partial Differential Equations, 2020)
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.