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

TL;DR

This paper improves decay rate estimates for solutions to the incompressible Navier-Stokes and Hall-MHD equations by refining analytical methods and considering initial data in specialized function spaces.

Contribution

It introduces refined decay rate results for weak solutions and solutions with initial data in Lei-Lin spaces for these fluid dynamics equations.

Findings

Enhanced decay rate estimates for weak solutions.

Decay rates established for solutions with Lei-Lin space initial data.

Refined Fourier splitting method applied to these 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.