Some Asymptotic Decay Results for Incompressible Viscous MHD Equations

We derive large time asymptotic decay results for spatial derivatives of solutions to the incompressible viscous magnetohydrodynamics equations in \({\mathbb {R}}^{n}\) ${\mathbb{R}}^n$ , \( 2 \le n \le 4 \) $2\le n\le 4$ . We derive both algebraic an exponential decay results under suitable assumptions on the solutions for each case. Moreover, we derive a long time behaviour result comparing such solutions with solutions for heat equation with the same initial conditions.