On asymptotic dynamics of solutions of the homogeneous Navier–Stokes equations Original Research Article

As the main result of the paper we prove that if ww is a strong global solution of the homogeneous Navier–Stokes equations in a smooth bounded domain View the MathML sourceΩ⊂R3 endowed with homogeneous Dirichlet boundary conditions then for every k,l,m∈N∪{0}k,l,m∈N∪{0} there exist C=C(k,l,m)C=C(k,l,m), t0=t0(k,l,m)≥0t0=t0(k,l,m)≥0 and δ0∈(0,1)δ0∈(0,1) such that View the MathML source‖dkwdtk(t)‖m,2≤C‖dlwdtl(t+δ)‖,∀t≥t0 and δ∈[0,δ0]. Turn MathJax on