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

TL;DR

This paper establishes the existence and decay rates over time of strong solutions to the Navier-Stokes equations within specific weighted infinity norm spaces, advancing understanding of fluid dynamics in unbounded domains.

Contribution

It provides new results on the existence and decay behavior of solutions in weighted $L^ abla$ spaces, extending previous work to more general weighted function spaces.

Findings

Proved existence of global strong solutions in weighted spaces.

Derived space-time decay rates for these solutions.

Extended the theory to broader weighted function 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 $L^\infty(\mathbb R^d,|x|^\gamma{\rm dx})\cap L^\infty(\mathbb R^d,|x|^\beta{\rm dx})$ spaces.