Air does have inertia since air has mass.
Anything that has mass which includes air does have inertia.
The inertia of air is that While speeding up, the air tends to remain at rest and gathers at the back.
Inertia is a force.
Inertia is a force that keeps stationary things and objects at rest and inertia keeps moving objects in motion at constant velocity.
Inertia is also the tendency of all objects to resist motion and ultimately stop moving.
The inertia is the resistance of any physical object to any change in its velocity.
Inertia also includes changes to the object's speed, or direction of motion.
And an aspect of this property is the tendency of objects to keep moving in a straight line at a constant speed.
In physics Inertia is a property of matter by which it continues in its existing state of rest or uniform motion in a straight line, unless that state is changed by an external force.