On analyticity and temporal decay rates of solutions to the viscous resistive Hall-MHD system

TL;DR

This paper investigates the analyticity and decay rates of solutions to the viscous resistive Hall-MHD system, showing solutions become analytic immediately and their analyticity radius grows like the square root of time, with bounds on derivative decay.

Contribution

It extends previous work by providing new bounds on the decay of higher order derivatives and demonstrating immediate analyticity with growth rate in the Hall-MHD equations.

Findings

Solutions become analytic immediately after t>0

Analyticity radius grows like √t over time

Bounds on decay of higher order derivatives established

Abstract

We address the analyticity and large time decay rates for strong solutions of the Hall-MHD equations. By Gevrey estimates, we show that the strong solution with small initial date in $H^r(\mathbb{R}^3)$ with $r>\f 52$ becomes analytic immediately after $t>0$, and the radius of analyticity will grow like $\sqrt{t}$ in time. Upper and lower bounds on the decay of higher order derivatives are also obtained, which extends the previous work by Chae and Schonbek (J. Differential Equations 255 (2013), 3971--3982).