On the temporal decay for the Hall-magnetohydrodynamic equations

TL;DR

This paper derives decay estimates over time for solutions to the Hall-magnetohydrodynamic equations, showing how solutions diminish algebraically in higher Sobolev norms for small initial data.

Contribution

It provides the first decay estimates for weak solutions to the Hall-MHD equations, including algebraic decay rates for higher order Sobolev norms.

Findings

Temporal decay estimates established

Algebraic decay for higher Sobolev norms proven

Decay results valid for small initial data

Abstract

We establish temporal decay estimates for weak solutions to the Hall-magnetohydrodynamic equations. With these estimates in hand we obtain algebraic time decay for higher order Sobolev norms of small initial data solutions.