Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License.
 adjective Of or pertaining to James Clerk Maxwell (18311879), Scottish theoretical
physicist andmathematician who made important contributions toelectromagnetic theory.  noun A supporter of James Clerk Maxwell.
Etymologies
from Wiktionary, Creative Commons Attribution/ShareAlike License
Examples

a spherically symmetric Maxwellian, which is analytic at the origin as the other example is not, and is not restricted to any quadrant of an ndimensional space, but has a similar “ridge” of maximal values.

Listen online or on 104. 4fm if you are in the magic land that can receive it via realactual Maxwellian radio waves.
Freaky Trigger and the Lollards of Pop – Series 3, Week 7  FreakyTrigger

They move randomly, with a Maxwellian velocity distribution

A universe without gravity waves would be about as nonsensical as one with Coulomb's law, Gauss' law, Faraday's law, but no Maxwellian EM waves.
ExtraGalactic Whopper Black Hole Breaks Distance Record  Universe Today

These result in large changes in magnetic fields that evolve in time, which are associated with large Maxwellian displacement currents, or equivalently electric fields.
Cluster Satellite Detects Rifts in Earth's Magnetic Field  Universe Today

They move randomly, with a Maxwellian velocity distribution

Holger Lyre (2004) extends Worrall's original example of the continuity between wave optics and electromagnetism by considering the relationship between Maxwellian electrodynamics and Quantum Electrodynamics.

If a Maxwellian demon exists, however, then it would appear possible the Clausius inequality would not hold.

This amounts to a situation in which some scholars say go ahead and do that arty farty Maxwellian stuff but not in my backyard or vice versa.

This is a wave equation similar to that for a Maxwellian electromagnetic wave with a source.
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