The existence and space-time decay rates of strong solutions to Navier-Stokes Equations in weighed $L^{\infty }(|x{|}^{\gamma }\mathrm{dx})\cap L^{\infty }(|x{|}^{\beta }\mathrm{dx})$ spaces

Abstract

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 $L^{\infty }({\mathbb{R}}^d,|x{|}^{\gamma }\mathrm{dx})\cap L^{\infty }({\mathbb{R}}^d,|x{|}^{\beta }\mathrm{dx})$ spaces.

arXiv comment17 pages