  The ideal magnetohydrodynamic equations are, roughly speaking, a quasi-linear
symmetric hyperbolic system of PDEs, but not all the unknowns play the same
role in this system. Indeed, in the regime of small magnetic fields, the
equations are close to the incompressible Euler equations. In the present
paper, we adopt this point of view to study questions linked with the lifespan
of strong solutions to the ideal magnetohydrodynamic equations. First of all,
we prove a continuation criterion in terms of the velocity field only.
Secondly, we refine the explicit lower bound for the lifespan of $2$-D flows
found in [11], by relaxing the regularity assumptions on the initial magnetic
field.
