  In this article, we show that the magneto-hydrodynamic system (MHD) in $\R^N$
with variable density, variable viscosity and variable conductivity has a local
weak solution in the Besov space $\dot
B^{\frac{N}{p_1}}_{p_1,1}(\R^N)\times\dot B^{\frac{N}{p_2}-1}_{p_2,1}(\R^N)
\times\dot B^{\frac{N}{p_2}-1}_{p_2,1}(\R^N)$ for all $1<p_2<+\infty$ and some
$1<p_1\leq\frac{2N}{3}$ if the initial density approaches a positive constant.
Moreover, this solution is unique if we impose the restrictive condition
$1<p_2\leq2N$. We prove also that the constructed solution exist globally in
time if the initial data are small enough. In particular, this allows us to
work in the frame of Besov space with negative regularity indices and this fact
is particularly important when the initial data are strong oscillating.
