The existence and space-time decay rates of strong solutions to   Navier-Stokes Equations in weighed $L^\infty(|x|^\gamma{\rm dx})\cap   L^\infty(|x|^\beta{\rm dx})$ spaces
  In this paper, we prove some results on theexistence and space-time decay rates of global strong solutions of the Cauchy problem for the Navier-Stokes equations in weighed $L^\infty(\mathbb R^d,|x|^\gamma{\rm dx})\cap L^\infty(\mathbb R^d,|x|^\beta{\rm dx})$ spaces. 
D. Q. Khai, N. M. Tri
math.AP