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

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).

17 pages

References in corpus (2)

• Singularity formation for the incompressible Hall-MHD equations without resistivity
• Space-time decay estimates for the incompressible viscous resistive Hall-MHD equations

Cited by in corpus (1)

• Global Existence and Optimal Decay Rates of Solutions for Compressible Hall-MHD Equations