Decay Rates of global weak solutions for the MHD equations in $\dot{\mbox{\boldmath{$H$}}}^{s}(\mathbb{R}^n)$

We show that t^{s/2} \Vert (\mbox{\boldmath u},\mbox{\boldmath b})(.,t)\Vert_{\dot{H}(\mathbb{R}^{n})} \rightarrow 0, as $t\rightarrow \infty$ for Leray solutions (\mbox{\boldmath u}, \mbox{\boldmath b})(.,t) of the incompressible MHD equations, where $2 \leq n \leq 4$ and $s \geq 0.$ As a corollary of main result described previously we have also that \lim_{t\rightarrow\infty} t^{\frac{n}{2} - \frac{n}{2q}} \Vert(\mbox{\boldmath u},\mbox{\boldmath b})(.,t)\Vert_{L^{q}(\mathbb{R}^{n})} = 0, 2\leq q\leq \infty.