LAUSR

We show that $t^{s/2} \| (\boldsymbol{u},\boldsymbol{b})(t) \|_{{\dot{H}^{s}(\mathbb{R}^{n})}} \to0 $ as $t \to\infty$ for global Leray solutions $(\boldsymbol{u},\boldsymbol{b})(t)$ of the incompressible MHD equations, where $2 \leq n \leq4$ and $s \geq0$ (real). We also provide some related results and, as a consequence, the following general decay property: $$ \lim_{t \to\infty} t^{\gamma(n,m,q)}\bigl\| \bigl(D^{m} \boldsymbol{u},D ^{m}\boldsymbol{b}\bigr) (t) \bigr\| _{\mathbf{L}^{q}(\mathbb{R}^{n})} = 0. $$ Where $\gamma(n,m,q) = \frac{n}{4} + \frac{m}{2} - \frac{n}{2q} $ , for each $2 \leq q \leq\infty$ , $n=2,3,4 $ and $m\geq0 $ integer.