I've seen similar questions asking about expressing Maxwell's equations with relativistic formulation, but my question is about the physical interpretation it may give for their conventional form.
I'm only familiar with the intuition of special relativity, but explanations I've seen for the origins of the magnetic field describe it as an electric field in a non-stationary reference frame caused by the length contraction of electrons increasing negative charge density. This results in a radial "electric" field in the reference frame of a moving charge that we view as caused by a magnetic field in a stationary frame. How do Maxwell's equations relating the curl of the electric and magnetic fields to the time derivatives of one another mathematically express this physical relationship?
Credit to https://www.youtube.com/watch?v=1FE0Z4lov7Y for image and beautiful basic explanation.
