On the temporal estimates for the incompressible Navier-Stokes equations and the Hall-magnetohydrodynamic equations

Abstract

In this paper, we derive decay rates for solutions to the incompressible Navier-Stokes equations and Hall-magnetohydrodynamic equations. We first improve the decay rate of weak solutions to these equations by refining the Fourier splitting method with initial data in the space of pseudo-measures. Additionally, we investigate these equations with initial data in the Lei-Lin spaces and establish decay rates for those solutions.

18 pages; v2: Theorems 1.4 and 1.5 revised with updated proofs; minor corrections; additional references