The Asymptotic Stability of the Generalized 3D Navier-Stokes Equations

Abstract

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∈Lp(0,∞;Bq,∞0(ℝ3)), (2α/p)+(3/q)=2α, 2<q<∞, 0<α<1, then every weak solution v(x,t) of the perturbed system converges asymptotically to u(x,t) as vt-utL2→0, t→∞.