The asymptotic stability of the generalized 3d navier-stokes equations

We study the stability issue of the generalized 3d navier-stokes equations. it is shown that if the weak solution u of the navier-stokes equations lies in the regular class u l p (0,∞; b q,∞ 0 (3)),(2 α / p) + (3 / q) = 2 α,2 < q < ∞,0 < α < 1,then every weak solution v (x,t) of the perturbed system converges asymptotically to u (x,t) as v t - u t l 2 → 0,t → ∞. © 2013 wen-juan wang and yan jia.