are there are 8 equations? I tried to break it into scalar bits and make new equations. The first two can be changed to make 1 scalar equation each and the second two equations break into 3 each using the definition of the curl operator.

Eq.1

Eq.2

Eq.3

Eq.4

Is this okay at a glance? Are all the terms scalars (if that's what a scalar equation is)?